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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. Deriv of sec^(-1)x
v3/2
-1/2
1/(|x| v(x^2-1))
e^x

2. cos p/3
0
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
1/2

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

4. Deriv of tan^(-1)x
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-1/2
-v2/2
1/(1+x^2 )

5. tan p/3
v3/2
v3
undefined
-v3

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

7. tan 4p/3
e^x
sec^2x
0
v3

8. cos 3p/4
-1/2
-v2/2
1/2
-1/v(1-x^2 )

9. tan 2p
1/v(1-x^2 )
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

10. sin p/3
v3/3
v2/2
0
v3/2

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

12. tan 5p/6
-v2/2
-sinx
-v3/3
-1

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

14. tan 3p/4
cosx
-1
0
v3

15. Deriv of f(x)=tanx is?
-v3
v3/3
sec^2x
a^u lna du/dx

16. cos 5p/4
1/(u ln a ) du/dx
1/(1+x^2 )
1
-v2/2

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

18. tan 5p/4
cosx
v3/2
1
0

19. cos p/6
a^u lna du/dx
-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

20. cos 5p/6
0
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
cosx
-v3/2

21. sin p/4
-v3/3
-1/2
v2/2
1

22. cos p
v3
-v3
0
-1

23. sin 7p/6
-1/2
1
1
1/v(1-x^2 )

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

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

26. Deriv of f(x)=cosx is?
f(x) = (u)(v) AND f'(x) = u'v + v'u
-sinx
-1/2
1

27. What is the Chain Rule? When can it be used?
1
0
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

28. 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
-1/v(1-x^2 )
-v2/2
0

29. cos 3p/2
1/u du/dx
0
-v3/2
-csc^2x

30. tan 7p/6
1/2
v3/3
-v3/3
1/(1+x^2 )

31. sin p/6
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
v2/2
-v2/2

32. tan p/4
f(x) = (u)(v) AND f'(x) = u'v + v'u
1
-v3/2
v2/2

33. Deriv of f(x)=sinx is?
cosx
0
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 )

34. sin 4p/3
0
-v3/2
v2/2
undefined

35. sin 5p/4
0
-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
-v3

36. Deriv of f(x)=secx is?
-1/(1+x^2 )
tanxsecx
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2

37. Guidelines for implicit differentiation
-v2/2
slope of the tangent line
-1/2
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

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

39. derivative
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v3/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
slope of the tangent line

40. Deriv of cot^(-1)x
-1/(1+x^2 )
v2/2
a^u lna du/dx
-1

41. What is the quotient rule?
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1/(u ln a ) du/dx
v2/2
tanxsecx

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

43. sin 5p/6
-1/2
1/2
-v3
tanxsecx

44. cos p/2
undefined
v3/2
1/v(1-x^2 )
0

45. Deriv of ln u
0
-1/2
sec^2x
1/u du/dx

46. what is the the limit definition of a derivative and what does it find?
-v3
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-sinx
-1/2

47. cos 7p/4
0
-1/2
v2/2
1

48. tan 3p/2
-1/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
undefined
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

49. Deriv of log_au=
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/(u ln a ) du/dx
1
1/2

50. tan 11p/6
-v3/3
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
v3
1/(u ln a ) du/dx

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AP Calculus 2

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