# Digitopolis - The Land of Numbers

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1. Differentiate

2. Differentiate

3. Differentiate

4. Differentiate

5. Differentiate

6. Differentiate

7. Differentiate

y=sin(x)
8. Differentiate

y=cos(x)
9. What is the Tangent Line Equation?
10. Differentiate

11. Differentiate

12. ReWrite

13. Rewrite

14. Differentiate

y=f(g(h(x)))
15. Differentiate

y=log(x)
16. Rewrite

17. Differentiate

y=sec(x)
18. Differentiate

y=log(g(x)
or
19. Rewrite

log(ab)=?
log(ab)=log(a)+log(b)
20. Rewrite

21. Rewrite

22. Differentiate

23. Differentiate

y=arcsin(x)
24. Differentiate

y=arcsec(x)
25. Rewrite

26. Differentiate

y=arctan(x)
27. Rewrite

28. ReWrite

29. Rewrite

30. Rewrite

31. Rewrite

32. Tangent Line Formula:

33. What is the Normal Line Formula?
34. Differentiate

y=tan(x)
35. Differentiate

y=csc(x)
36. Differentiate

y=cot(x)
37. Differentiate

y=sec(x)
38. Rewrite

sin(a+b)=?
sin(a+b)=cos(a)sin(b)+sin(a)cos(b)
39. Rewrite

sin(2x)=?
sin(2x)=sin(x+x)

=

sin(x)cos(x)+cos(x)sin(x)
40. Solve

41. Solve

42. Rewrite

cos(x)sin(x)=?
43. Rewrite

sin(x)sec(x)=?
sin(x)sec(x)=tan(x)
44. Functions:

In what "form" will a function become a Vertical Asymptote?
45. Functions

In what "form" will a function have a hole?
When a point is undefined.

46. Functions:

Describe a Polynomial
A smooth, well behaved function.

Ex:

47. Functions:

Describe a Rational Function.
A polynomial multiplied, or divided by, another polynomial.

Ex:

48. Functions:

Describe an exponential function.
A function whose variable is the exponent of the function.

49. Functions:

Describe a Horizontal Asymptote.
When a function's limit as it approaches positive or negative infinity is a real number, that is it's Horizontal Asymptote.

50. Rewrite

51. Functions:

What are some of the other terms for a prime function?

The derivative of a function.

The rate of change(at a given point) of a function.

The slope of a function.

The velocity of a function.
52. Differentiate

Rewrite and Differentiate:

Since conventional methods would have messy results, rewrite your function.

53. Trig Functions

Give 3 different trig variations for this function:

Sin(x)
Tan(x)Cos(x)

1/Csc(x)

Tan(x)/Sec(x)
54. l' Hopital's Rule

In what two function scenarios can you implement the l' Hopital's Rule?
When the functions are of the forms:

• 0/0
• or
• Infinity/Infinity
55. Volume

What is the volume of a cone?
56. l' Hopital's Rule

What effect does l' Hopital's Rule have on your function?
57. l' Hopital's Rule

What are the 5 indeterminate "forms"?
• 1-
• 2-
• 3-
• 4-
• 5-
58. Functions

Extreme values of a function only occur at what points(p)?

or when P is a boundary point of f's domain.
59. Multiplicity

What occurs when a function passes through a critical point where the multiplicity is even?
It changes signs.

• From + to -
• or
• From - to +
60. Area

What is the Area of a triangle?
61. Area

What is the Area of a circle?
62. Circumference

What is the circumference of a circle?
63. Memory Tools

Some Old Hags...
Can't Always Hide

Their Old Age
64. Optimization

What points are of most interest to you when working with Optimization?
Critical Points and Endpoints.
65. Volume

What is the volume of a cylinder?
66. Volume

What is the volume of a sphere?
67. Area

What is the area of a sphere?
68. Diameter

What is the diameter of a circle or sphere?
69. Formula

What is the distance formula?
70. Formula

What is the Area of a square?
A=xy
71. Logarithms

72. Functions

73. Logarithms

Log(1)=?
Log(1)=0
74. Formula

What is the area of a cylinder?
• The area of the top and bottom:
• Plus the area of the sides:

75. Formula

What is the volume of a cube?
 Author: mattrcherry ID: 211333 Card Set: Digitopolis - The Land of Numbers Updated: 2013-04-11 05:20:16 Tags: Poopenheim Folders: Description: This is a Calculous Study Guide for my Cal 1 class. Show Answers: