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DiffCalcWeek1

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Estas con las transparencias, en Keynote, de la primera semana de mi curso de Cálculo diferencial.

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DiffCalcWeek1

  1. 1. Day 11. Course Guidelines2. Critical Path to Success
  2. 2. Critical Path to Success!!A student who wants to succeed in this course will: • Always be on time for class.
  3. 3. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed.
  4. 4. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed.
  5. 5. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed. Notebooks
  6. 6. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed. Notebooks
  7. 7. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed. Pencil Notebooks
  8. 8. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed. Pencil Notebooks
  9. 9. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed. Pencil Notebooks Pen(s)
  10. 10. Critical Path to Success!!A student who wants to succeed in this course will: • Always attempt ALL their homework assignments.
  11. 11. Critical Path to Success!!A student who wants to succeed in this course will: • Review their class notes every night before going to bed.
  12. 12. The Curve of Forgetting... Describes how we retain or get rid of information that we take in. It´s based on a one-hour lecture.
  13. 13. Critical Path to Success!!A student who wants to succeed in this course will: • Always ask LOTS of questions about anything they don’t understand.
  14. 14. Critical Path to Success!!A student who wants to succeed in this course will: • Always gets extra help from the teacher when they feel they are falling behind.
  15. 15. Factoring Review.
  16. 16. Before we start...
  17. 17. Before we start...1. What is a prime number?
  18. 18. Before we start...1. What is a prime number?2. What’s factoring?
  19. 19. Before we start...1. What is a prime number?2. What’s factoring?3. Why do we need factoring?
  20. 20. Day 2Opener.1. What is the first step in any factoring problem?2. What is the first step to factor -x2 + 8x - 15?3. On a test, Luis Gonzalez wrote the following, but the teacher considered it to be incomplete. Explain why 15x2 - 21x - 18 = (5x + 3)(3x - 6)
  21. 21. Factoring Strategy.Step 1. Always check for the ___________________ first.
  22. 22. Factoring Strategy. greatest common factorStep 1. Always check for the ___________________ first.
  23. 23. Factoring Strategy.Step 2. Is the expression a -termed expression? If yes, then try one of these three forms: 1. ________________________: 2. ________________________: 3. ________________________:
  24. 24. Factoring Strategy.Step 2. Is the expression a two -termed expression? If yes, then try one of these three forms: 1. ________________________: 2. ________________________: 3. ________________________:
  25. 25. Factoring Strategy.Step 2. Is the expression a two -termed expression? If yes, then try one of these three forms: 1. a2 - b2 = (a + b)(a - b) ________________________: 2. ________________________: 3. ________________________:
  26. 26. Factoring Strategy.Step 2. Is the expression a two -termed expression? If yes, then try one of these three forms: 1. a2 - b2 = (a + b)(a - b) ________________________: 2. a3 + b3 = (a + b)(a2 - ab + b2) ________________________: 3. ________________________:
  27. 27. Factoring Strategy.Step 2. Is the expression a two -termed expression? If yes, then try one of these three forms: 1. a2 - b2 = (a + b)(a - b) ________________________: 2. a3 + b3 = (a + b)(a2 - ab + b2) ________________________: a3 - b3 = (a - b)(a2 + ab + b2) 3. ________________________:
  28. 28. Factoring Strategy.Step 3. If it is a -termed expression (or trinomial), it may fall into one of these groups: 1.The coefficient of is 1. Example: ________________. Find two numbers whose sum is ______ and whose product is ______. They are ______ and ______:
  29. 29. Factoring Strategy.Step 3. If it is a three -termed expression (or trinomial), it may fall into one of these groups: 1.The coefficient of is 1. Example: ________________. Find two numbers whose sum is ______ and whose product is ______. They are ______ and ______:
  30. 30. Factoring Strategy.Step 3. If it is a three -termed expression (or trinomial), it may fall into one of these groups: 1.The coefficient of x is 1. Example: ________________. Find two numbers whose sum is ______ and whose product is ______. They are ______ and ______:
  31. 31. Factoring Strategy.Step 3. If it is a three -termed expression (or trinomial), it may fall into one of these groups: x2 - 17x - 60 1.The coefficient of x is 1. Example: ________________. Find two numbers whose sum is ______ and whose product is ______. They are ______ and ______:
  32. 32. Factoring Strategy.Step 3. If it is a three -termed expression (or trinomial), it may fall into one of these groups: x2 - 17x - 60 1.The coefficient of x is 1. Example: ________________. -17 Find two numbers whose sum is ______ and whose product is ______. They are ______ and ______:
  33. 33. Factoring Strategy.Step 3. If it is a three -termed expression (or trinomial), it may fall into one of these groups: x2 - 17x - 60 1.The coefficient of x is 1. Example: ________________. -17 Find two numbers whose sum is ______ and whose -60 product is ______. They are ______ and ______:
  34. 34. Factoring Strategy.Step 3. If it is a three -termed expression (or trinomial), it may fall into one of these groups: x2 - 17x - 60 1.The coefficient of x is 1. Example: ________________. -17 Find two numbers whose sum is ______ and whose -60 -20 product is ______. They are ______ and ______:
  35. 35. Factoring Strategy.Step 3. If it is a three -termed expression (or trinomial), it may fall into one of these groups: x2 - 17x - 60 1.The coefficient of x is 1. Example: ________________. -17 Find two numbers whose sum is ______ and whose -60 -20 3 product is ______. They are ______ and ______:
  36. 36. Factoring Strategy. 2. T h e c o e f f i c i e n t o f is not 1. Example: ________________. a. Find the product of first and last coefficients: ___________ = _____. b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  37. 37. Factoring Strategy. 2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e : ________________. a. Find the product of first and last coefficients: ___________ = _____. b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  38. 38. Factoring Strategy. 2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e : 6x2 - 7x - 3 ________________. a. Find the product of first and last coefficients: ___________ = _____. b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  39. 39. Factoring Strategy. 2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e : 6x2 - 7x - 3 ________________. a. Find the product of first and last coefficients: (6)(-3) ___________ = _____. b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  40. 40. Factoring Strategy. 2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e : 6x2 - 7x - 3 ________________. a. Find the product of first and last coefficients: (6)(-3) ___________ = _____. -18 b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  41. 41. Factoring Strategy. 2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e : 6x2 - 7x - 3 ________________. a. Find the product of first and last coefficients: (6)(-3) ___________ = _____. -18 -18 b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  42. 42. Factoring Strategy. 2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e : 6x2 - 7x - 3 ________________. a. Find the product of first and last coefficients: (6)(-3) ___________ = _____. -18 -18 b. Look for two numbers whose product is ______ and -7 whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  43. 43. Factoring Strategy. 2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e : 6x2 - 7x - 3 ________________. a. Find the product of first and last coefficients: (6)(-3) ___________ = _____. -18 -18 b. Look for two numbers whose product is ______ and -7 -9 whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  44. 44. Factoring Strategy. 2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e : 6x2 - 7x - 3 ________________. a. Find the product of first and last coefficients: (6)(-3) ___________ = _____. -18 -18 b. Look for two numbers whose product is ______ and -7 -9 whose sum is _____: _____ and ______. 2 c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  45. 45. Factoring Strategy. 2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e : 6x2 - 7x - 3 ________________. a. Find the product of first and last coefficients: (6)(-3) ___________ = _____. -18 -18 b. Look for two numbers whose product is ______ and -7 -9 whose sum is _____: _____ and ______. 2 c. Write the expression as four terms: 6x2 - 9x +2x - 3 d. Proceed to use Step 4 as follows:
  46. 46. Factoring Strategy.Step 4. If it is a -termed expression, try factoring by grouping. Example:
  47. 47. Factoring Strategy.Step 4. If it is a four -termed expression, try factoring by grouping. Example:
  48. 48. Factoring Strategy.Step 4. If it is a four -termed expression, try factoring by grouping. Example: 2x2 - 3xy - 4x + 6y
  49. 49. Exercises.Factor each expression completely. 4 2 3 1. x − 9x 2. x − 27 3 2 3. x + 8 4. 4t + 16t + 16 2 2 5. y − 9y + 20 6. 6m + 5m − 4
  50. 50. Homework 1.Baldor, Algebra:Exercise106, Problems 9, 18, 27, 36, 47, 54, 73, 83, 91, 98, 109 and128, p. 171
  51. 51. Day 3Opener.A person is standing at the top of a building, and throws a ballupwards from a height of 60 ft, with an initial velocity of 30 ftper second. How long will it take for the ball to reach a heightof 25 ft from the floor? 1 2Use the formula h = gt + v0t + h0 2
  52. 52. Quadratic Formula.If ax2 +bx + c = 0 and a ≠ 1, then 2 −b ± b − 4ac x= 2a
  53. 53. Exercises.Solve the equations. Use the quadratic formula: 2 2t + 8t + 8 = 0 x = 2x − 3
  54. 54. Trigonometry review.What is a reference angle?
  55. 55. Trigonometry review.What is a reference angle? The reference angle for θ is the acute angle θR that the terminal side of θ makes with the x-axis.
  56. 56. Trigonometry review.What is a reference angle? The reference angle for θ is the acute angle θR that the terminal side of θ makes with the x-axis.
  57. 57. Find the reference angle θR for θ, and sketch θ and θR in standardposition.
  58. 58. Find the reference angle θR for θ, and sketch θ and θR in standardposition. a) -240o
  59. 59. Find the reference angle θR for θ, and sketch θ and θR in standardposition. a) -240o b) θ = 5π/6
  60. 60. Homework 2.Baldor, Algebra:Exercise 266, odd numbered problems, p. 450
  61. 61. Day 4Find the exact values of sin θ, cos θ and tan θ if(a) θ = 5π/6 (b) θ = 315o
  62. 62. The Fundamental Identities.1. The Reciprocal Identities. 1 1 1 csc α = sec α = cot α = sin α cos α tan α2. The Tangent and Cotangent Identities. sin α cos α tan α = cot α = cos α sin α3. The Pythagorean Identities. sin 2 α + cos 2 α = 1
  63. 63. Verifying Trigonometric Identities.Show that the following equation is an identity bytransforming the left-hand side into the right-hand side: (sec x + tan x )(1− sin x ) = cos x
  64. 64. tan x + cos x = sec x + cot x sin x
  65. 65. Day 5 Class Activity.

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