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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. cos p/6
-1/2
-1/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
v3/2

2. tan 5p/4
-v3/3
v3/2
1
v2/2

3. Deriv of ln u
1/u du/dx
1
slope of the tangent line
-1/v(1-x^2 )

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

5. Deriv of csc^(-1)x
1/(1+x^2 )
-1/(1+x^2 )
-v2/2
-1/(|x| v(x^2-1))

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

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

8. Deriv of f(x)=tanx is?
1/v(1-x^2 )
v3/2
-sinx
sec^2x

9. cos p/3
1/(1+x^2 )
-v2/2
1/2
-1/2

10. cos p
-1
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-1/2
-v3

11. When do derivatives not exist?
-v3/3
v3
e^x
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

12. tan 3p/4
-1
v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-v2/2

13. cos 2p
1
-1
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
v3/2

14. What is the Chain Rule? When can it be used?
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
1
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
undefined

15. tan p/2
v3/2
slope of the tangent line
-1/2
undefined

16. Explicit differentiation
v3/2
1/v(1-x^2 )
v3/3
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

17. Deriv of a^u
-v3/2
a^u lna du/dx
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-1/2

18. cos p/4
1
v2/2
-1
-cscxcotx

19. sin 5p/3
1
-v3/2
0
e^x

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

21. Deriv of tan^(-1)x
v3/2
1/(1+x^2 )
tanxsecx
0

22. sin 2p/3
undefined
v3/2
0
1/2

23. sin 5p/6
1/2
-v3/2
1
-1/2

24. What is the product rule?

25. sin p/2
v2/2
1
-v3/2
-1

26. Deriv of sin^(-1)x
-1
-1/(1+x^2 )
1/v(1-x^2 )
v3/3

27. tan 5p/3
-v2/2
-v3
f(x) = (u)(v) AND f'(x) = u'v + v'u
0

28. tan p/4
v3
tanxsecx
1
-1

29. sin 3p/2
-v3/3
undefined
1/(|x| v(x^2-1))
-1

30. Deriv of sec^(-1)x
1/(|x| v(x^2-1))
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
f(x) = (u)(v) AND f'(x) = u'v + v'u
-1/2

31. Deriv of log_au=
1/(1+x^2 )
cosx
-csc^2x
1/(u ln a ) du/dx

32. tan p
1
-v3
-1
0

33. sin 2p
v3/2
0
f(x) = (u)(v) AND f'(x) = u'v + v'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

34. Deriv of f(x)=sinx is?
v2/2
1/v(1-x^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
cosx

35. Deriv of f(x)=csc is?
-cscxcotx
-v2/2
-v3/2
-1

36. tan 3p/2
-v2/2
0
v3/3
undefined

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

38. sin p/4
1/2
-csc^2x
0
v2/2

39. Deriv of cos^(-1)x
-v3/2
cosx
a^u lna du/dx
-1/v(1-x^2 )

40. cos 7p/4
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
0
undefined
v2/2

41. cos 5p/3
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
sec^2x
0

42. sin 7p/6
-1/2
-v3/2
cosx
a^u lna du/dx

43. cos 3p/2
1
-v3/2
0
e^x

44. cos 3p/4
1/v(1-x^2 )
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-v2/2
-1/2

45. Guidelines for implicit differentiation
0
v3/2
v2/2
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

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

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

48. sin 3p/4
v2/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3/2
1/(u ln a ) du/dx

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

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