Liz
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The document provides the solution to a calculus word problem involving a particle moving along a curve. The problem asks for (a) the rate of change of the y-coordinate when the particle is at (1,2) and the x-coordinate is increasing at 6 units/s, and (b) whether the particle is rising or falling at that instant. The solution takes three steps: (1) taking the derivative of the equation of the curve, (2) plugging in the given values (1,2) and dx/dt = 6, and (3) solving for dy/dt, which is -60/7 units/s. Therefore, the y-coordinate is decreasing,
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This document discusses solving systems of linear equations by elimination. It provides examples of eliminating variables with opposite coefficients as well as multiplying equations to create opposite coefficients. The key steps are to multiply one equation by a number to create opposite coefficients, add or subtract the equations to eliminate one variable, then solve for the remaining variable and back substitute to solve for the other. Elimination avoids lengthy substitution and allows direct solving of systems of equations.
Graphs of the Sine and Cosine Functions Lecture
More: www.PinoyBIX.org
Lesson Objectives
Able to plot the different Trigonometric Graphs
Graph of Sine Function (y = f(x) = sinx)
Graph of Cosine Function (y = f(x) = cosx)
Define the Maximum and Minimum value in a graph
Generalized Trigonometric Functions
Graphs of y = sinbx
Graphs of y = sin(bx + c)
Could find the Period of Trigonometric Functions
Could find the Amplitude of Trigonometric Functions
Variations in the Trigonometric Functions
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Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
C2 st lecture 3 handout
This document provides an overview of the topics covered in Lecture 3 of a Calculus I course, including:
- Evaluating functions and using trial and improvement to find solutions to equations
- Differentiating polynomial expressions and finding the gradient of a curve at a given point
- Key terms like function, polynomial, curve, tangent, and derivative
- Examples of using trial and improvement to find solutions between values and determining points where the gradient of a curve is zero
Developing Expert Voices
The student reflects on completing a math project for their calculus course as a way to study for an upcoming exam. They acknowledge that they procrastinated significantly but were able to cover a broad range of calculus concepts through multi-step word problems selected from different units. While the assignment did not dramatically increase their knowledge, it helped reinforce some details and connections between topics. The student resolves to select deadlines more wisely and stop procrastinating for future projects.
15.3---Graphs-of-Quad-Functions.pptx
The document provides information about quadratic functions including:
- How to find the roots, intercept, turning point, and whether the turning point is a maximum or minimum value by analyzing the quadratic equation.
- Examples of using factorizing, completing the square, and setting the equation equal to 0 to find the roots.
- How to sketch the graph of a quadratic function using its equation by plotting the roots, intercept, turning point, and labeling whether the turning point is a max or min.
Sect1 2
This section introduces general and particular solutions to differential equations of the form y' = f(x) through direct integration and evaluation of constants. Examples provided include:
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2) Integrating y' = (x - 2)^2 and applying x = 2, y = 1 yields y(x) = (1/3)(x - 2)^3.
3) Six more examples of first-order differential equations are worked through to find their general solutions.
The Application of Derivatives
This document discusses several topics related to calculus including:
1) Derivatives of position, velocity, and acceleration and how they relate to each other.
2) An example problem calculating velocity from a position function.
3) The Mean Value Theorem and how to apply it to find critical points of a function.
4) How the first and second derivatives of a function relate to critical points, maxima, minima, and points of inflection or concavity.
5) Related rates problems and how to set them up using derivatives and relationships between variables.
Amth250 octave matlab some solutions (2)
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This document provides an overview of solving systems of linear equations through three methods: graphing, substitution, and elimination. It defines systems of linear equations as two or more linear equations with the same variables, where the point of intersection is the solution. Examples are worked through for each solving method. Graphing involves putting the equations in y-intercept form and finding the point where the lines intersect on a graph. Substitution involves solving one equation for a variable and substituting it into the other equation. Elimination involves adding or subtracting the equations to eliminate a variable and then solving for the remaining variable.
_12_ - Exponential Functions (1).pdf
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MA 243 Calculus III Fall 2015 Dr. E. JacobsAssignmentsTh.docx
MA 243 Calculus III Fall 2015 Dr. E. Jacobs
Assignments
These assignments are keyed to Edition 7E of James Stewart’s “Calculus” (Early Transcendentals)
Assignment 1. Spheres and Other Surfaces
Read 12.1 - 12.2 and 12.6
You should be able to do the following problems:
Section 12.1/Problems 11 - 18, 20 - 22 Section 12.6/Problems 1 - 48
Hand in the following problems:
1. The following equation describes a sphere. Find the radius and the coordinates of the center.
x2 + y2 + z2 = 2(x + y + z) + 1
2. A particular sphere with center (−3, 2, 2) is tangent to both the xy-plane and the xz-plane.
It intersects the xy-plane at the point (−3, 2, 0). Find the equation of this sphere.
3. Suppose (0, 0, 0) and (0, 0, −4) are the endpoints of the diameter of a sphere. Find the
equation of this sphere.
4. Find the equation of the sphere centered around (0, 0, 4) if the sphere passes through the
origin.
5. Describe the graph of the given equation in geometric terms, using plain, clear language:
z =
√
1 − x2 − y2
Sketch each of the following surfaces
6. z = 2 − 2
√
x2 + y2
7. z = 1 − y2
8. z = 4 − x − y
9. z = 4 − x2 − y2
10. x2 + z2 = 16
Assignment 2. Dot and Cross Products
Read 12.3 and 12.4
You should be able to do the following problems:
Section 12.3/Problems 1 - 28 Section 12.4/Problems 1 - 32
Hand in the following problems:
1. Let u⃗ =
⟨
0, 1
2
,
√
3
2
⟩
and v⃗ =
⟨√
2,
√
3
2
, 1
2
⟩
a) Find the dot product b) Find the cross product
2. Let u⃗ = j⃗ + k⃗ and v⃗ = i⃗ +
√
2 j⃗.
a) Calculate the length of the projection of v⃗ in the u⃗ direction.
b) Calculate the cosine of the angle between u⃗ and v⃗
3. Consider the parallelogram with the following vertices:
(0, 0, 0) (0, 1, 1) (1, 0, 2) (1, 1, 3)
a) Find a vector perpendicular to this parallelogram.
b) Use vector methods to find the area of this parallelogram.
4. Use the dot product to find the cosine of the angle between the diagonal of a cube and one of
its edges.
5. Let L be the line that passes through the points (0, −
√
3 , −1) and (0,
√
3 , 1). Let θ be the
angle between L and the vector u⃗ = 1√
2
⟨0, 1, 1⟩. Calculate θ (to the nearest degree).
Assignment 3. Lines and Planes
Read 12.5
You should be able to do the following problems:
Section 12.5/Problems 1 - 58
Hand in the following problems:
1a. Find the equation of the line that passes through (0, 0, 1) and (1, 0, 2).
b. Find the equation of the plane that passes through (1, 0, 0) and is perpendicular to the line in
part (a).
2. The following equation describes a straight line:
r⃗(t) = ⟨1, 1, 0⟩ + t⟨0, 2, 1⟩
a. Find the angle between the given line and the vector u⃗ = ⟨1, −1, 2⟩.
b. Find the equation of the plane that passes through the point (0, 0, 4) and is perpendicular to
the given line.
3. The following two lines intersect at the point (1, 4, 4)
r⃗ = ⟨1, 4, 4⟩ + t⟨0, 1, 0⟩ r⃗ = ⟨1, 4, 4⟩ + t⟨3, 5, 4⟩
a. Find the angle between the two lines.
b. Find the equation of the plane that contains every point o ...
Calculus Assignment Help
I am Eugeny G. I am a Calculus Assignment Expert at mathsassignmenthelp.com. I hold a Master's in Mathematics from, Columbia University. I have been helping students with their assignments for the past 8 years. I solve assignments related to Calculus.
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You can also call on +1 678 648 4277 for any assistance with Calculus Assignment.
Two Dimensional Motion and Vectors
This document provides an overview of two-dimensional motion and vectors. It introduces scalars and vectors, and discusses how to add vectors graphically or using trigonometric functions. Projectile motion is also summarized, noting that the vertical and horizontal components of a projectile's motion are independent, and can be analyzed separately using kinematic equations. Examples are provided for adding vectors, resolving vectors into components, and solving projectile motion problems.
Projectile motion
The document discusses projectile motion and provides sample problems to illustrate the concepts. It begins by defining projectile motion and describing the forces acting on a projectile. It then presents the kinematic equations for the horizontal and vertical motion of a projectile. Several sample problems are worked out applying these equations to calculate values like minimum launch speed, projectile impact location and time, and velocity at impact.
Projectile motion
The document discusses projectile motion and provides sample problems to illustrate the concepts. It begins by defining projectile motion and describing the forces acting on a projectile. It then presents the kinematic equations for the horizontal and vertical motion of a projectile. Several sample problems are worked out applying these equations to calculate values like minimum launch speed, projectile impact location and time, and velocity at impact.
MATHS - Linear equation in two variable (Class - X) Maharashtra Board
MATHS - Linear equation in two variable
(Class - X)
Maharashtra Board
Equations/Expressions
Word Problem
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