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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.
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 cot^(-1)x
-1/(1+x^2 )
1/2
-csc^2x
-sinx

2. sin p/3
v3/2
a^u lna du/dx
-v3/3
-1

3. sin 2p
0
-cscxcotx
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
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

4. Deriv of ln u
1/u du/dx
undefined
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1

5. cos 5p/6
undefined
slope of the tangent line
1/(1+x^2 )
-v3/2

6. cos 7p/4
v2/2
-1/2
0
f(x) = (u)(v) AND f'(x) = u'v + v'u

7. Deriv of f(x)=tanx is?
sec^2x
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v2/2
1/v(1-x^2 )

8. cos p/3
1/2
-csc^2x
0
-1

9. What is the product rule?
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2
v3/2
-1/(1+x^2 )

10. cos 3p/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1
-v3/3
0

11. derivative
v3/2
-v2/2
1
slope of the tangent line

12. what is the the limit definition of a derivative and what does it find?
0
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1/(1+x^2 )
-1/2

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

14. Deriv of csc^(-1)x
-1/(|x| v(x^2-1))
0
1/2
1

15. tan p/2
-v3/2
tanxsecx
a^u lna du/dx
undefined

16. Deriv of f(x)=sinx is?
cosx
-v2/2
1
a^u lna du/dx

17. cos 5p/3
0
v3
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

18. Guidelines for implicit differentiation
-v2/2
1/v(1-x^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
v2/2

19. tan 7p/4
-1
-v2/2
v3/3
1/(1+x^2 )

20. cos 2p
1
-v3
-v3/2
-v2/2

21. What is the Alternate definition of a derivative and what does it find?
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
-sinx
-cscxcotx
-v2/2

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

23. sin 5p/4
v3/2
-v2/2
-1/2
1/(1+x^2 )

24. tan 3p/2
-csc^2x
0
undefined
-1

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

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

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

28. cos 7p/6
-1/(1+x^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
-v3/2
-v3/3

29. Deriv of f(x)=csc is?
-1/v(1-x^2 )
-cscxcotx
-1/2
v3/2

30. Explicit differentiation
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
v3/2
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

31. Deriv of tan^(-1)x
0
1/(1+x^2 )
0
0

32. sin 5p/6
-sinx
v3/2
-cscxcotx
1/2

33. tan p/3
v2/2
v3
v3/2
0

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

35. Deriv of sec^(-1)x
1/(|x| v(x^2-1))
cosx
v3/3
sec^2x

36. Deriv of e^x
e^x
-v3/2
0
1

37. Deriv of a^u
f(x) = (u)(v) AND f'(x) = u'v + v'u
0
v3/2
a^u lna du/dx

38. tan 11p/6
-v2/2
-1/v(1-x^2 )
-v3/3
0

39. sin 2p/3
1
0
-sinx
v3/2

40. sin 11p/6
-1/2
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
0

41. sin 7p/6
v3/2
0
-1/2
tanxsecx

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

43. What is the Chain Rule? When can it be used?
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-cscxcotx
-v3/3

44. tan 3p/4
-1
-v3/3
1/(1+x^2 )
1/u du/dx

45. sin 3p/4
-v3/3
v3
v3/2
v2/2

46. tan 4p/3
-1
slope of the tangent line
1
v3

47. tan 5p/3
-v3
0
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1/(|x| v(x^2-1))

48. cos 3p/4
1/v(1-x^2 )
1/u du/dx
-v2/2
-1

49. sin 7p/4
-v2/2
-1
undefined
v3/2

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

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AP Calculus 2

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