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AP Calculus 2

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Deriv of f(x)=cotx is?
v3/3
-csc^2x
-v2/2
1/2

2. cos 3p/4
v3/3
-v3/2
-v2/2
1/2

3. Deriv of f(x)=tanx is?
sec^2x
-v2/2
1/2
1/(u ln a ) du/dx

4. cos 5p/4
v3/2
-v2/2
-1/2
-v3

5. sin 3p/2
-1
-v2/2
1/v(1-x^2 )
undefined

6. sin 4p/3
1
v3/2
0
-v3/2

7. Deriv of sec^(-1)x
1
1/(|x| v(x^2-1))
-csc^2x
e^x

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

9. Deriv of f(x)=secx is?
v3
undefined
tanxsecx
-1/(1+x^2 )

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

11. tan 3p/2
-v3/2
1/(u ln a ) du/dx
v2/2
undefined

12. sin p/4
-v2/2
0
-1/v(1-x^2 )
v2/2

13. cos 11p/6
v3/2
sec^2x
-1
f(x) = (u)(v) AND f'(x) = u'v + v'u

14. sin p/6
1
-cscxcotx
1/2
v3

15. cos p/2
a^u lna du/dx
-v3/2
0
-v3/2

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

17. sin 5p/6
1
1/2
-sinx
1/v(1-x^2 )

18. cos 5p/6
-v2/2
1/2
-v3/2
-v2/2

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

20. tan 3p/4
v3/3
v2/2
-v2/2
-1

21. tan 5p/3
-v3
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
0
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

22. sin 7p/6
0
-1
1
-1/2

23. What is the product rule?

24. sin 2p
1/2
-1
0
-v3/3

25. tan 5p/6
-v3/3
1
v3/3
-1

26. cos 2p/3
-1
v3/2
-1/2
-csc^2x

27. Deriv of log_au=
1/(u ln a ) du/dx
undefined
1/(|x| v(x^2-1))
v3/2

28. cos 2p
1
v3
-1/(|x| v(x^2-1))
1/u du/dx

29. tan p/4
0
-v3/2
cosx
1

30. cos p/6
v3/2
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
1/(1+x^2 )
v2/2

31. cos 4p/3
-1/2
-1
1/2
-v2/2

32. sin 11p/6
-1/2
1/u du/dx
e^x
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

33. tan p/2
-v2/2
-csc^2x
-1/(1+x^2 )
undefined

34. tan 4p/3
v3
v2/2
-1
-cscxcotx

35. sin 7p/4
-v2/2
0
-1/(|x| v(x^2-1))
v3/2

36. Deriv of tan^(-1)x
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1/(1+x^2 )
1/2
e^x

37. cos 7p/4
v3/2
v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
0

38. cos p/3
1/2
sec^2x
-1/(1+x^2 )
-1/2

39. cos 3p/2
1
0
-v3/2
-1/v(1-x^2 )

40. tan 2p/3
-v2/2
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
-v3
1/(u ln a ) du/dx

41. Deriv of cot^(-1)x
e^x
-1/(1+x^2 )
-v3/2
-1

42. 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
a^u lna du/dx
1
1/v(1-x^2 )

43. Deriv of ln u
v3/3
1/u du/dx
1/2
-1/2

44. Deriv of a^u
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
v3
-v3/3
a^u lna du/dx

45. Guidelines for implicit differentiation
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
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) 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
1

46. Implicit differentiation
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
v3/3
0
-1

47. sin 2p/3
1/u du/dx
-v2/2
v3/2
-1

48. cos 5p/3
1/2
v2/2
-v3/2
1

49. cos p/4
v3/2
v2/2
a^u lna du/dx
-1/2

50. tan 2p
-1
-v3/2
-1/2
0