The document presents a T-chart that compares different concepts such as likes/hates, fun/have to do, and regret/proud of across typical/unusual experiences. It then provides strategies and examples for generating ideas, adding details to sentences, and using "show and tell" techniques for writing. The rest of the document consists of a word web that connects different values like happiness, friendship, love, courage, and more.
Natalie D.C. is halfway through her UK tour promoting her new album. Despite being in the middle of a long tour, she maintains high energy and optimism. She acknowledges that touring can be tiring, but says she's happy doing what she loves. Her bandmates sometimes find her upbeat attitude annoying, and band dynamics can be challenging living together on tour, but she enjoys exploring new places and making memories through photography. She answers fans' questions, discussing finding her identity in school and choosing not to conform, and says her favorite songs off the new album are "Undisclosed Party Invite" for its lyrics and "WTF" for being fun to play live.
The document summarizes Joe and Danielle's wedding ceremony and reception. It describes the exchanging of vows between Joe and Danielle, with Steve giving Danielle away. The reception included the bridal party entrance, the first dance, father-daughter and mother-son dances, toasts from the maid of honor and best man, cake cutting, bouquet and garter toss traditions, dancing, and concludes with congratulations to the newly married couple.
The document discusses the story of Terry Fox, a Canadian hero who lost his leg to cancer but then ran across Canada to raise money and awareness for cancer research. It provides background on Fox's life, the obstacles he faced during his Marathon of Hope run across Canada, and the legacy and honors he has received for his courage and determination in bringing attention to cancer research. The document ends by describing Fox as an inspiration who continues to be remembered through annual fundraising runs in his name.
This Sporlan training module will demonstrate the proper use of the pressure-temperature pocket card or wall chart. It will illustrate how pressure and temperature measurements from a refrigeration unit may be useful for system analysis. Included will be a discussion about superheated vapor, subcooled liquid and saturated vapor/liquid mixtures in an operating refrigeration system.
The document is a lecture on inverse trigonometric functions from a Calculus I class at New York University. It defines inverse trigonometric functions as the inverses of restricted trigonometric functions, gives their domains and ranges, and discusses their derivatives. The document also provides examples of evaluating inverse trigonometric functions.
Implicit differentiation allows us to find slopes of lines tangent to curves that are not graphs of functions. Almost all of the time (yes, that is a mathematical term!) we can assume the curve comprises the graph of a function and differentiate using the chain rule.
Natalie D.C. is halfway through her UK tour promoting her new album. Despite being in the middle of a long tour, she maintains high energy and optimism. She acknowledges that touring can be tiring, but says she's happy doing what she loves. Her bandmates sometimes find her upbeat attitude annoying, and band dynamics can be challenging living together on tour, but she enjoys exploring new places and making memories through photography. She answers fans' questions, discussing finding her identity in school and choosing not to conform, and says her favorite songs off the new album are "Undisclosed Party Invite" for its lyrics and "WTF" for being fun to play live.
The document summarizes Joe and Danielle's wedding ceremony and reception. It describes the exchanging of vows between Joe and Danielle, with Steve giving Danielle away. The reception included the bridal party entrance, the first dance, father-daughter and mother-son dances, toasts from the maid of honor and best man, cake cutting, bouquet and garter toss traditions, dancing, and concludes with congratulations to the newly married couple.
The document discusses the story of Terry Fox, a Canadian hero who lost his leg to cancer but then ran across Canada to raise money and awareness for cancer research. It provides background on Fox's life, the obstacles he faced during his Marathon of Hope run across Canada, and the legacy and honors he has received for his courage and determination in bringing attention to cancer research. The document ends by describing Fox as an inspiration who continues to be remembered through annual fundraising runs in his name.
This Sporlan training module will demonstrate the proper use of the pressure-temperature pocket card or wall chart. It will illustrate how pressure and temperature measurements from a refrigeration unit may be useful for system analysis. Included will be a discussion about superheated vapor, subcooled liquid and saturated vapor/liquid mixtures in an operating refrigeration system.
The document is a lecture on inverse trigonometric functions from a Calculus I class at New York University. It defines inverse trigonometric functions as the inverses of restricted trigonometric functions, gives their domains and ranges, and discusses their derivatives. The document also provides examples of evaluating inverse trigonometric functions.
Implicit differentiation allows us to find slopes of lines tangent to curves that are not graphs of functions. Almost all of the time (yes, that is a mathematical term!) we can assume the curve comprises the graph of a function and differentiate using the chain rule.
This document summarizes a calculus lecture on linear approximations. It provides examples of using the tangent line to approximate the sine function at different points. Specifically, it estimates sin(61°) by taking linear approximations about 0 and about 60°. The linear approximation about 0 is x, giving a value of 1.06465. The linear approximation about 60° uses the fact that the sine is √3/2 and the derivative is √3/2 at π/3, giving a better approximation than using 0.
This document contains lecture notes on related rates from a Calculus I class at New York University. It begins with announcements about assignments and no class on a holiday. It then outlines the objectives of learning to use derivatives to understand rates of change and model word problems. Examples are provided, including an oil slick problem worked out in detail. Strategies for solving related rates problems are discussed. Further examples on people walking and electrical resistors are presented.
Lesson 14: Derivatives of Logarithmic and Exponential FunctionsMel Anthony Pepito
The document discusses conventions for defining exponential functions with exponents other than positive integers, such as negative exponents, fractional exponents, and exponents of zero. It defines exponential functions with these exponent types in a way that maintains important properties like ax+y = ax * ay. The goal is to extend the definition of exponential functions beyond positive integer exponents in a principled way.
This document contains lecture notes on exponential growth and decay from a Calculus I class at New York University. It begins with announcements about an upcoming review session, office hours, and midterm exam. It then outlines the topics to be covered, including the differential equation y=ky, modeling population growth, radioactive decay including carbon-14 dating, Newton's law of cooling, and continuously compounded interest. Examples are provided of solving various differential equations representing exponential growth or decay. The document explains that many real-world situations exhibit exponential behavior due to proportional growth rates.
This document is from a Calculus I class lecture on L'Hopital's rule given at New York University. It begins with announcements and objectives for the lecture. It then provides examples of limits that are indeterminate forms to motivate L'Hopital's rule. The document explains the rule and when it can be used to evaluate limits. It also introduces the mathematician L'Hopital and applies the rule to examples introduced earlier.
The document provides an overview of curve sketching in calculus including objectives, rationale, theorems for determining monotonicity and concavity, and a checklist for graphing functions. It then gives examples of graphing cubic and quartic functions step-by-step, demonstrating how to analyze critical points, inflection points, and asymptotic behavior to create the curve. The examples illustrate applying differentiation rules to determine monotonicity from the derivative sign chart and concavity from the second derivative test.
This document is a section from a Calculus I course at New York University covering maximum and minimum values. It begins with announcements about exams and assignments. The objectives are to understand the Extreme Value Theorem and Fermat's Theorem, and use the Closed Interval Method to find extreme values. The document then covers the definitions of extreme points/values and the statements of the Extreme Value Theorem and Fermat's Theorem. It provides examples to illustrate the necessity of the hypotheses in the theorems. The focus is on using calculus concepts like continuity and differentiability to determine maximum and minimum values of functions on closed intervals.
This document is the notes from a Calculus I class at New York University covering Section 4.2 on the Mean Value Theorem. The notes include objectives, an outline, explanations of Rolle's Theorem and the Mean Value Theorem, examples of using the theorems, and a food for thought question. The key points are that Rolle's Theorem states that if a function is continuous on an interval and differentiable inside the interval, and the function values at the endpoints are equal, then there exists a point in the interior where the derivative is 0. The Mean Value Theorem similarly states that if a function is continuous on an interval and differentiable inside, there exists a point where the average rate of change equals the instantaneous rate of
This document discusses the definite integral and its properties. It begins by stating the objectives of computing definite integrals using Riemann sums and limits, estimating integrals using approximations like the midpoint rule, and reasoning about integrals using their properties. The outline then reviews the integral as a limit of Riemann sums and how to estimate integrals. It also discusses properties of the integral and comparison properties. Finally, it restates the theorem that if a function is continuous, the limit of Riemann sums is the same regardless of the choice of sample points.
The document summarizes the steps to solve optimization problems using calculus. It begins with an example of finding the rectangle with maximum area given a fixed perimeter. It works through the solution, identifying the objective function, variables, constraints, and using calculus techniques like taking the derivative to find critical points. The document then outlines Polya's 4-step method for problem solving and provides guidance on setting up optimization problems by understanding the problem, introducing notation, drawing diagrams, and eliminating variables using given constraints. It emphasizes using the Closed Interval Method, evaluating the function at endpoints and critical points to determine maximums and minimums.
The document is about calculating areas and distances using calculus. It discusses approximating areas of curved regions by dividing them into rectangles and letting the number of rectangles approach infinity. It provides examples of calculating areas of basic shapes like rectangles, parallelograms, and triangles. It then discusses Archimedes' work approximating the area under a parabola by inscribing sequences of triangles. The objectives are to compute areas using limits of approximating rectangles and to compute distances as limits of approximating time intervals.
This document is from a Calculus I class at New York University and covers antiderivatives. It begins with announcements about an upcoming quiz. The objectives are to find antiderivatives of simple functions, remember that a function whose derivative is zero must be constant, and solve rectilinear motion problems. It then outlines finding antiderivatives through tabulation, graphically, and with rectilinear motion examples. The document provides examples of finding antiderivatives of power functions by using the power rule in reverse.
- The document is about evaluating definite integrals and contains sections on: evaluating definite integrals using the evaluation theorem, writing antiderivatives as indefinite integrals, interpreting definite integrals as net change over an interval, and examples of computing definite integrals.
- It discusses properties of definite integrals such as additivity and comparison properties, and provides examples of definite integrals that can be evaluated using known area formulas or by direct computation of antiderivatives.
Here are the key points about g given f:
- g represents the area under the curve of f over successive intervals of the x-axis
- As x increases over an interval, g will increase if f is positive over that interval and decrease if f is negative
- The concavity (convexity or concavity) of g will match the concavity of f over each interval
In summary, the area function g, as defined by the integral of f, will have properties that correspond directly to the sign and concavity of f over successive intervals of integration.
This document provides information about a Calculus I course taught by Professor Matthew Leingang at the Courant Institute of Mathematical Sciences at NYU. The course will include weekly lectures, recitations, homework assignments, quizzes, a midterm exam, and a final exam. Grades will be determined based on exam, homework, and quiz scores. The required textbook is available in hardcover, looseleaf, or online formats through the campus bookstore or WebAssign. Students are encouraged to contact the professor or TAs with any questions.
The document is a section from a Calculus I course at NYU from June 22, 2010. It discusses using the substitution method to evaluate indefinite integrals. Specifically, it provides an example of using the substitution u=x^2+3 to evaluate the integral of (x^2+3)^3 4x dx. The solution transforms the integral into an integral of u^3 du and evaluates it to be 1/4 u^4 + C.
This document outlines information about a Calculus I course taught by Professor Matthew Leingang at the Courant Institute of Mathematical Sciences. It provides details on the course staff, contact information for the professor, an overview of assessments including homework, quizzes, a midterm and final exam. Grading breakdown is also included, as well as information on purchasing the required textbook and accessing the course on Blackboard. The document aims to provide students with essential logistical information to succeed in the Calculus I course.
This document contains lecture notes from a Calculus I class at New York University on September 14, 2010. The notes cover announcements, guidelines for written homework, a rubric for grading homework, examples of good and bad homework, and objectives for the concept of limits. The bulk of the document discusses the heuristic definition of a limit using an error-tolerance game approach, provides examples to illustrate the game, and outlines the path to a precise definition of a limit.
This document contains lecture notes on the concept of limit from a Calculus I course at New York University. It includes announcements about homework and deadlines. It then discusses guidelines for written homework assignments and a rubric for grading. The bulk of the document explains the concept of limit intuitively through an "error-tolerance game" and provides examples to illustrate the idea. It aims to build an informal understanding of limits before providing a precise definition.
No, this is not a function because the same input of 2 is mapped to two different outputs of 4 and 5. For a relation to be a function, each input must map to a unique output.
V63.0121.021/041, Calculus I (NYU) Section 1.1 Functions September 8, 2010 17 / 33
This document summarizes a calculus lecture on linear approximations. It provides examples of using the tangent line to approximate the sine function at different points. Specifically, it estimates sin(61°) by taking linear approximations about 0 and about 60°. The linear approximation about 0 is x, giving a value of 1.06465. The linear approximation about 60° uses the fact that the sine is √3/2 and the derivative is √3/2 at π/3, giving a better approximation than using 0.
This document contains lecture notes on related rates from a Calculus I class at New York University. It begins with announcements about assignments and no class on a holiday. It then outlines the objectives of learning to use derivatives to understand rates of change and model word problems. Examples are provided, including an oil slick problem worked out in detail. Strategies for solving related rates problems are discussed. Further examples on people walking and electrical resistors are presented.
Lesson 14: Derivatives of Logarithmic and Exponential FunctionsMel Anthony Pepito
The document discusses conventions for defining exponential functions with exponents other than positive integers, such as negative exponents, fractional exponents, and exponents of zero. It defines exponential functions with these exponent types in a way that maintains important properties like ax+y = ax * ay. The goal is to extend the definition of exponential functions beyond positive integer exponents in a principled way.
This document contains lecture notes on exponential growth and decay from a Calculus I class at New York University. It begins with announcements about an upcoming review session, office hours, and midterm exam. It then outlines the topics to be covered, including the differential equation y=ky, modeling population growth, radioactive decay including carbon-14 dating, Newton's law of cooling, and continuously compounded interest. Examples are provided of solving various differential equations representing exponential growth or decay. The document explains that many real-world situations exhibit exponential behavior due to proportional growth rates.
This document is from a Calculus I class lecture on L'Hopital's rule given at New York University. It begins with announcements and objectives for the lecture. It then provides examples of limits that are indeterminate forms to motivate L'Hopital's rule. The document explains the rule and when it can be used to evaluate limits. It also introduces the mathematician L'Hopital and applies the rule to examples introduced earlier.
The document provides an overview of curve sketching in calculus including objectives, rationale, theorems for determining monotonicity and concavity, and a checklist for graphing functions. It then gives examples of graphing cubic and quartic functions step-by-step, demonstrating how to analyze critical points, inflection points, and asymptotic behavior to create the curve. The examples illustrate applying differentiation rules to determine monotonicity from the derivative sign chart and concavity from the second derivative test.
This document is a section from a Calculus I course at New York University covering maximum and minimum values. It begins with announcements about exams and assignments. The objectives are to understand the Extreme Value Theorem and Fermat's Theorem, and use the Closed Interval Method to find extreme values. The document then covers the definitions of extreme points/values and the statements of the Extreme Value Theorem and Fermat's Theorem. It provides examples to illustrate the necessity of the hypotheses in the theorems. The focus is on using calculus concepts like continuity and differentiability to determine maximum and minimum values of functions on closed intervals.
This document is the notes from a Calculus I class at New York University covering Section 4.2 on the Mean Value Theorem. The notes include objectives, an outline, explanations of Rolle's Theorem and the Mean Value Theorem, examples of using the theorems, and a food for thought question. The key points are that Rolle's Theorem states that if a function is continuous on an interval and differentiable inside the interval, and the function values at the endpoints are equal, then there exists a point in the interior where the derivative is 0. The Mean Value Theorem similarly states that if a function is continuous on an interval and differentiable inside, there exists a point where the average rate of change equals the instantaneous rate of
This document discusses the definite integral and its properties. It begins by stating the objectives of computing definite integrals using Riemann sums and limits, estimating integrals using approximations like the midpoint rule, and reasoning about integrals using their properties. The outline then reviews the integral as a limit of Riemann sums and how to estimate integrals. It also discusses properties of the integral and comparison properties. Finally, it restates the theorem that if a function is continuous, the limit of Riemann sums is the same regardless of the choice of sample points.
The document summarizes the steps to solve optimization problems using calculus. It begins with an example of finding the rectangle with maximum area given a fixed perimeter. It works through the solution, identifying the objective function, variables, constraints, and using calculus techniques like taking the derivative to find critical points. The document then outlines Polya's 4-step method for problem solving and provides guidance on setting up optimization problems by understanding the problem, introducing notation, drawing diagrams, and eliminating variables using given constraints. It emphasizes using the Closed Interval Method, evaluating the function at endpoints and critical points to determine maximums and minimums.
The document is about calculating areas and distances using calculus. It discusses approximating areas of curved regions by dividing them into rectangles and letting the number of rectangles approach infinity. It provides examples of calculating areas of basic shapes like rectangles, parallelograms, and triangles. It then discusses Archimedes' work approximating the area under a parabola by inscribing sequences of triangles. The objectives are to compute areas using limits of approximating rectangles and to compute distances as limits of approximating time intervals.
This document is from a Calculus I class at New York University and covers antiderivatives. It begins with announcements about an upcoming quiz. The objectives are to find antiderivatives of simple functions, remember that a function whose derivative is zero must be constant, and solve rectilinear motion problems. It then outlines finding antiderivatives through tabulation, graphically, and with rectilinear motion examples. The document provides examples of finding antiderivatives of power functions by using the power rule in reverse.
- The document is about evaluating definite integrals and contains sections on: evaluating definite integrals using the evaluation theorem, writing antiderivatives as indefinite integrals, interpreting definite integrals as net change over an interval, and examples of computing definite integrals.
- It discusses properties of definite integrals such as additivity and comparison properties, and provides examples of definite integrals that can be evaluated using known area formulas or by direct computation of antiderivatives.
Here are the key points about g given f:
- g represents the area under the curve of f over successive intervals of the x-axis
- As x increases over an interval, g will increase if f is positive over that interval and decrease if f is negative
- The concavity (convexity or concavity) of g will match the concavity of f over each interval
In summary, the area function g, as defined by the integral of f, will have properties that correspond directly to the sign and concavity of f over successive intervals of integration.
This document provides information about a Calculus I course taught by Professor Matthew Leingang at the Courant Institute of Mathematical Sciences at NYU. The course will include weekly lectures, recitations, homework assignments, quizzes, a midterm exam, and a final exam. Grades will be determined based on exam, homework, and quiz scores. The required textbook is available in hardcover, looseleaf, or online formats through the campus bookstore or WebAssign. Students are encouraged to contact the professor or TAs with any questions.
The document is a section from a Calculus I course at NYU from June 22, 2010. It discusses using the substitution method to evaluate indefinite integrals. Specifically, it provides an example of using the substitution u=x^2+3 to evaluate the integral of (x^2+3)^3 4x dx. The solution transforms the integral into an integral of u^3 du and evaluates it to be 1/4 u^4 + C.
This document outlines information about a Calculus I course taught by Professor Matthew Leingang at the Courant Institute of Mathematical Sciences. It provides details on the course staff, contact information for the professor, an overview of assessments including homework, quizzes, a midterm and final exam. Grading breakdown is also included, as well as information on purchasing the required textbook and accessing the course on Blackboard. The document aims to provide students with essential logistical information to succeed in the Calculus I course.
This document contains lecture notes from a Calculus I class at New York University on September 14, 2010. The notes cover announcements, guidelines for written homework, a rubric for grading homework, examples of good and bad homework, and objectives for the concept of limits. The bulk of the document discusses the heuristic definition of a limit using an error-tolerance game approach, provides examples to illustrate the game, and outlines the path to a precise definition of a limit.
This document contains lecture notes on the concept of limit from a Calculus I course at New York University. It includes announcements about homework and deadlines. It then discusses guidelines for written homework assignments and a rubric for grading. The bulk of the document explains the concept of limit intuitively through an "error-tolerance game" and provides examples to illustrate the idea. It aims to build an informal understanding of limits before providing a precise definition.
No, this is not a function because the same input of 2 is mapped to two different outputs of 4 and 5. For a relation to be a function, each input must map to a unique output.
V63.0121.021/041, Calculus I (NYU) Section 1.1 Functions September 8, 2010 17 / 33
7. LIKE FUN
Things I Like Things I Do For Fun
CARE INTEREST
Things I Care About Things I’m Interested In
8. LIKE FUN
Things I Like Things I Do For Fun
• money
• baseball
• take trips
• hip hop
• go to the mall
• clothes
• surf the internet
• pizza
• talk on the phone
• video games
CARE INTEREST
Things I Care About Things I’m Interested In
• my family
• getting a job
• my pets
• computers
• my friends
• cars
• safe neighborhood
• going to college
• people being treated fairly
10. IDEA DETAILS
A sentence that needs more support What your audience needs to know
11. IDEA DETAILS
A sentence that needs more support What your audience needs to know
I was stopped in traffic on
I had a huge car accident. the freeway when a truck came up
behind me.
I heard his engine roar and I knew he
was going too fast.
He didn’t notice I was stopped so he
didn’t slow down until it was too late.
He slammed on his brakes but still hit
me.
Glass and metal went flying
everywhere.
I was scared. I didn’t know if I was
going to get hurt.
12. IDEA DETAILS
A sentence that needs more support What your audience needs to know
My car needed $5000 of The back end on the right side of my
repair work. car was completely flattened.
I couldn’t open the trunk or the right
rear passenger side door.
The car wobbled a lot.
I took the car to my mechanic and
he recommended a guy who does
body work.
He had the car for over a week and
and when it was done it looked
brand new.
He charged $5000 dollars for the
repair but my insurance paid for it.
14. TELL SHOW
Just say it very simply Describe it in detail
My basketball game had a It all came down to the final few
strange and exciting ending. seconds. We were behind my one
point, 57-56. We were going to go
for one shot. I was supposed to pass
it to Robert. He was our best
shooter, but he was blocked by two
players on the other team. If I didn’t
pass or shoot it, the ref would blow
the whistle and the other team
would take possession. O chucked it
as hard as I could toward the basket.
Everyone’s hands reached up for the
ball. No one could get their hands
on it. Then, a miracle happened. The
ball hit one of their players in the
head and bounced in the hoop as
the buzzer when off.
16. TELL VISUALIZE & LIST
The lake looked really nice
that morning
SHOW
17. TELL VISUALIZE & LIST
The lake looked really nice water smooth and clear
that morning
SHOW
18. TELL VISUALIZE & LIST
The lake looked really nice water smooth and clear
that morning mist rising up
SHOW
19. TELL VISUALIZE & LIST
The lake looked really nice water smooth and clear
that morning mist rising up
fish jumping
SHOW
20. TELL VISUALIZE & LIST
The lake looked really nice water smooth and clear
that morning mist rising up
fish jumping
sun coming up
SHOW
21. TELL VISUALIZE & LIST
The lake looked really nice water smooth and clear
that morning mist rising up
fish jumping
sun coming up
our boat
SHOW
22. TELL VISUALIZE & LIST
The lake looked really nice water smooth and clear
that morning mist rising up
fish jumping
sun coming up
our boat
a group of ducks
SHOW
23. TELL VISUALIZE & LIST
The lake looked really nice water smooth and clear
that morning mist rising up
fish jumping
sun coming up
our boat
a group of ducks
it was cold
SHOW
24. TELL VISUALIZE & LIST
The lake looked really nice water smooth and clear
that morning mist rising up
fish jumping
sun coming up
our boat
a group of ducks
it was cold
SHOW
The water was as smooth as glass and clear enough that we could se almost all
the way to the bottom. Thin wisps of mist rose up all around us as our boat
glided slowly along. Occasionally, a fish would jump but we’d never actually see
it. We’d turn our heads at the sounds of the splash just in time to see the
circles of little waves expanding outward where the fish had come down.
Closer to shore, a group of ducks cut a v-shape in the quiet water as they
swam along. It was cold but he sun was coming up and I know that in a few
minutes int would start to get warm.
39. Happiness often
Friendship occasionally
Love
Courage
40. Happiness often
Friendship occasionally
Love never
Courage
41. Happiness often
Friendship occasionally
Love never
Courage usually
42. Happiness often
Friendship occasionally
Love never
Courage usually
sometimes
43. Happiness often
Friendship occasionally
Love never
Courage usually
sometimes
rarely
44. Happiness often
Friendship occasionally
Love never
Courage usually
sometimes
rarely
unexpectedly
45. Happiness often
Friendship occasionally
Love never
Courage usually
sometimes
rarely
unexpectedly
slowly
46. Happiness often
Friendship occasionally
Love never
Courage usually
sometimes
rarely
unexpectedly
slowly
simply
47. Happiness often
Friendship occasionally
Love never
Courage usually
sometimes
rarely
unexpectedly
slowly
simply
completely
48. Happiness often
Friendship occasionally
Love never
Courage usually
sometimes
rarely
unexpectedly
slowly
simply
completely
totally
49. Happiness often
Friendship occasionally
Love never
Courage usually
Honesty sometimes
rarely
unexpectedly
slowly
simply
completely
totally
50. Happiness often
Friendship occasionally
Love never
Courage usually
Honesty sometimes
Deception rarely
unexpectedly
slowly
simply
completely
totally
51. Happiness often
Friendship occasionally
Love never
Courage usually
Honesty sometimes
Deception rarely
Talent unexpectedly
slowly
simply
completely
totally
52. Happiness often
Friendship occasionally
Love never
Courage usually
Honesty sometimes
Deception rarely
Talent unexpectedly
Success slowly
simply
completely
totally
53. Happiness often
Friendship occasionally
Love never
Courage usually
Honesty sometimes
Deception rarely
Talent unexpectedly
Success slowly
Pride simply
completely
totally
54. Happiness often
Friendship occasionally
Love never
Courage usually
Honesty sometimes
Deception rarely
Talent unexpectedly
Success slowly
Pride simply
Honor completely
totally
55. Happiness often
Friendship occasionally
Love never
Courage usually
Honesty sometimes
Deception rarely
Talent unexpectedly
Success slowly
Pride simply
Honor completely
Hatred totally
56. Happiness often
Friendship occasionally
Love never
Courage usually
Honesty sometimes
Deception rarely
Talent unexpectedly
Success slowly
Pride simply
Honor completely
Hatred totally
Power
57. Happiness often just shows up
Friendship occasionally
Love never
Courage usually
Honesty sometimes
Deception rarely
Talent unexpectedly
Success slowly
Pride simply
Honor completely
Hatred totally
Power
58. Happiness often just shows up
Friendship occasionally requires effort
Love never
Courage usually
Honesty sometimes
Deception rarely
Talent unexpectedly
Success slowly
Pride simply
Honor completely
Hatred totally
Power
59. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
Courage usually
Honesty sometimes
Deception rarely
Talent unexpectedly
Success slowly
Pride simply
Honor completely
Hatred totally
Power
60. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
hurts others
Courage usually
Honesty sometimes
Deception rarely
Talent unexpectedly
Success slowly
Pride simply
Honor completely
Hatred totally
Power
61. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
hurts others
Courage usually
helps others
Honesty sometimes
Deception rarely
Talent unexpectedly
Success slowly
Pride simply
Honor completely
Hatred totally
Power
62. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
hurts others
Courage usually
helps others
Honesty sometimes makes a difference
Deception rarely
Talent unexpectedly
Success slowly
Pride simply
Honor completely
Hatred totally
Power
63. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
hurts others
Courage usually
helps others
Honesty sometimes makes a difference
Deception rarely sneaks up on you
Talent unexpectedly
Success slowly
Pride simply
Honor completely
Hatred totally
Power
64. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
hurts others
Courage usually
helps others
Honesty sometimes makes a difference
Deception rarely sneaks up on you
Talent unexpectedly changes people
Success slowly
Pride simply
Honor completely
Hatred totally
Power
65. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
hurts others
Courage usually
helps others
Honesty sometimes makes a difference
Deception rarely sneaks up on you
Talent unexpectedly changes people
Success slowly takes over
Pride simply
Honor completely
Hatred totally
Power
66. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
hurts others
Courage usually
helps others
Honesty sometimes makes a difference
Deception rarely sneaks up on you
Talent unexpectedly changes people
Success slowly takes over
Pride simply is achieved
Honor completely
Hatred totally
Power
67. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
hurts others
Courage usually
helps others
Honesty sometimes makes a difference
Deception rarely sneaks up on you
Talent unexpectedly changes people
Success slowly takes over
Pride simply is achieved
scars the soul
Honor completely
Hatred totally
Power
68. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
hurts others
Courage usually
helps others
Honesty sometimes makes a difference
Deception rarely sneaks up on you
Talent unexpectedly changes people
Success slowly takes over
Pride simply is achieved
scars the soul
Honor completely overpowers people
Hatred totally
Power
69. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
hurts others
Courage usually
helps others
Honesty sometimes makes a difference
Deception rarely sneaks up on you
Talent unexpectedly changes people
Success slowly takes over
Pride simply is achieved
scars the soul
Honor completely overpowers people
Hatred totally changes nothing
Power
70. Happiness often just shows up
Friendship occasionally requires effort
Love never is misunderstood
hurts others
Courage usually
helps others
Honesty sometimes makes a difference
Deception rarely sneaks up on you
Talent unexpectedly changes people
Success slowly takes over
Pride simply is achieved
scars the soul
Honor completely overpowers people
Hatred totally changes nothing
Power sort of