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AP Calculus 2

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. what is the the limit definition of a derivative and what does it find?

2. derivative
slope of the tangent line
-v2/2
sec^2x
v3/2

3. tan 2p/3
v3
v2/2
-1/2
-v3

4. What is the Alternate definition of a derivative and what does it find?

5. cos p/2
0
1/2
f^' (a)=lim-(x?a)??(f(x)-f(a))/(x-a)? - It is finding the slope of the tangent line at a particular x-value
-csc^2x

6. cos 2p/3
-1/2
very clear; the variable y is explicitly written as a function of x and it only works when you can solve for the function explicitly E.g. y=3x^2-5
-1
0

7. tan p/3
f^' (a)=lim-(x?a)??(f(x)-f(a))/(x-a)? - It is finding the slope of the tangent line at a particular x-value
-1/2
v3
-1/(1+x^2 )

8. Deriv of tan^(-1)x
v3
undefined
-1/(|x| v(x^2-1))
1/(1+x^2 )

9. sin p/6
-v3/3
1/v(1-x^2 )
1/2
undefined

10. tan 4p/3
v3
-v3
-v3/3
1)At a "spot" of discontinuity (pt.(hole) - infinite(VA) - jump) 2)At a corner 3)At a cusp(sharp pt.) 4)At a vertical tangent line

11. sin p/2
1/2
-v2/2
1
-v3/3

12. Implicit differentiation
1/2
-1
-1/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

13. tan p/4
-v2/2
1)At a "spot" of discontinuity (pt.(hole) - infinite(VA) - jump) 2)At a corner 3)At a cusp(sharp pt.) 4)At a vertical tangent line
-v3/2
1

14. cos 2p
1/(1+x^2 )
0
1
0

15. sin 2p
1/2
0
e^x
1) find the derivative of both sides of the function 2) put all terms with a y prime on the same side (y prime aka derivative of y) 3) factor out a y 4) solve for y prime

16. Deriv of cos^(-1)x
1/2
-1/v(1-x^2 )
0
v3

17. What is the product rule?

18. cos 5p/6
-v3/2
-sinx
cosx
e^x

19. sin 3p/2
undefined
v3/2
-1
v2/2

20. cos 3p/4
-v3
-v3/2
-1/(1+x^2 )
-v2/2

21. sin 4p/3
-v2/2
v3/3
-1/(|x| v(x^2-1))
-v3/2

22. sin 7p/6
cosx
-1/2
-1
a^u lna du/dx

23. cos 7p/6
f^' (a)=lim-(x?a)??(f(x)-f(a))/(x-a)? - It is finding the slope of the tangent line at a particular x-value
-v3/3
-v3/2
-1/(1+x^2 )

24. sin 2p/3
1
1/v(1-x^2 )
v3/2
-v3/3

25. sin p/4
-v2/2
v2/2
undefined
-v3/3

26. Guidelines for implicit differentiation
1) find the derivative of both sides of the function 2) put all terms with a y prime on the same side (y prime aka derivative of y) 3) factor out a y 4) solve for y prime
0
v3/3
a^u lna du/dx

27. sin 3p/4
-1/(|x| v(x^2-1))
0
v2/2
-v3/3

28. Deriv of f(x)=csc is?
1/v(1-x^2 )
1
-1/(|x| v(x^2-1))
-cscxcotx

29. Deriv of log_au=
0
-v2/2
1/(|x| v(x^2-1))
1/(u ln a ) du/dx

30. tan p
0
1/(u ln a ) du/dx
-1/2
1/2

31. cos p/4
v3/3
v2/2
v3/2
-v3/2

32. What is the Chain Rule? When can it be used?
v3/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
a^u lna du/dx
1/2

33. cos 4p/3
-v3
0
-1/2
v3/3

34. sin p/3
slope of the tangent line
-csc^2x
-1/2
v3/2

35. Deriv of sec^(-1)x
cosx
-v2/2
1
1/(|x| v(x^2-1))

36. Deriv of f(x)=cosx is?
1/v(1-x^2 )
-1
1)At a "spot" of discontinuity (pt.(hole) - infinite(VA) - jump) 2)At a corner 3)At a cusp(sharp pt.) 4)At a vertical tangent line
-sinx

37. cos p/6
v3/2
-v3
-v2/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

38. tan 11p/6
-v3/2
-v3/3
v2/2
1/2

39. tan 5p/6
v3
-v3/3
-1/2
-1

40. Deriv of f(x)=cotx is?
-csc^2x
0
1/2
-1/v(1-x^2 )

41. tan p/2
-1/2
-1/(1+x^2 )
undefined
-1

42. tan p/6
very clear; the variable y is explicitly written as a function of x and it only works when you can solve for the function explicitly E.g. y=3x^2-5
v3/3
v3/2
f^' (a)=lim-(x?a)??(f(x)-f(a))/(x-a)? - It is finding the slope of the tangent line at a particular x-value

43. tan 3p/2
1/2
1)At a "spot" of discontinuity (pt.(hole) - infinite(VA) - jump) 2)At a corner 3)At a cusp(sharp pt.) 4)At a vertical tangent line
undefined
-1/2

44. tan 7p/4
0
-v3/2
-1
-v3/3

45. cos 11p/6
v3/2
-v3/2
a^u lna du/dx
v2/2

46. cos 7p/4
v2/2
1/(u ln a ) du/dx
-1/2
0

47. Deriv of f(x)=sinx is?
0
1/v(1-x^2 )
cosx
v3

48. When do derivatives not exist?
1)At a "spot" of discontinuity (pt.(hole) - infinite(VA) - jump) 2)At a corner 3)At a cusp(sharp pt.) 4)At a vertical tangent line
-v2/2
-v2/2
v3/3

49. cos p/3
0
1/(1+x^2 )
1/2
e^x

50. sin 7p/4
-v2/2
v2/2
-cscxcotx
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)