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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. sin 5p/3
-v3/2
-1/(|x| v(x^2-1))
-1
1/(|x| v(x^2-1))

2. Explicit differentiation
1/(|x| v(x^2-1))
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
0

3. Deriv of f(x)=cosx is?
-1/2
-v3/2
cosx
-sinx

4. Deriv of ln u
-csc^2x
1/u du/dx
1/(|x| v(x^2-1))
1

5. sin 2p/3
v2/2
v3/2
1
1/2

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

7. Deriv of f(x)=tanx is?
-1/v(1-x^2 )
0
-v3/2
sec^2x

8. Deriv of a^u
-csc^2x
a^u lna du/dx
tanxsecx
-1

9. Deriv of log_au=
-sinx
-1/(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
1/(u ln a ) du/dx

10. cos p/4
1/(1+x^2 )
v2/2
-v3/3
0

11. What is the Alternate definition of a derivative and what does it find?
-cscxcotx
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
-1/2

12. tan 7p/4
1/2
1/u du/dx
-1
0

13. Deriv of f(x)=csc is?
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
-cscxcotx
1/(1+x^2 )
v2/2

14. Implicit differentiation
-v2/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
v3/2
-1/(|x| v(x^2-1))

15. cos 2p
v3/2
v3
1/(u ln a ) du/dx
1

16. sin 5p/6
0
1/2
undefined
v2/2

17. tan 3p/2
a^u lna du/dx
-v3/2
undefined
1/2

18. What is the Chain Rule? When can it be used?
v2/2
1/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
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

19. cos 3p/2
-1
0
-v3/2
-v3

20. sin 2p
-v3/2
v3
0
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

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

22. cos 7p/6
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1
-v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

23. cos 5p/4
undefined
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
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

24. tan 5p/3
-v3
1/v(1-x^2 )
-v3/2
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

25. tan p
v3
-v3
0
1/2

26. sin p/3
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
v3/2
1/2
-v2/2

27. tan p/6
-v3
-sinx
1
v3/3

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

29. What is the quotient rule?
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
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-v3/2
-1

30. Deriv of cos^(-1)x
-v3/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v2/2
-1/v(1-x^2 )

31. tan 5p/6
-v3/3
1/(|x| v(x^2-1))
-v3/2
1

32. When do derivatives not exist?
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)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
cosx

33. cos p/6
v3/2
v3
a^u lna du/dx
1

34. cos p/3
v3
1/2
1
-v3/2

35. tan 7p/6
v3/3
1
1/2
0

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

37. Deriv of csc^(-1)x
v3/3
v3/2
-1
-1/(|x| v(x^2-1))

38. tan 4p/3
1/2
-1/2
v3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

39. Deriv of e^x
-1
e^x
-v3/2
-csc^2x

40. sin 7p/4
e^x
tanxsecx
-v3/3
-v2/2

41. tan 3p/4
f(x) = (u)(v) AND f'(x) = u'v + v'u
1
0
-1

42. sin p/4
-v3/2
-v2/2
-1/2
v2/2

43. sin 7p/6
0
v3/2
v3/2
-1/2

44. Deriv of f(x)=secx is?
1/v(1-x^2 )
v3/2
slope of the tangent line
tanxsecx

45. sin 3p/4
v2/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3/2
-1/(1+x^2 )

46. sin p/2
v3/2
v2/2
1
v3/2

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

48. 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
1/u du/dx
1/2
v3

49. cos 2p/3
-1/2
0
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
v3

50. cos 11p/6
v3/2
1/u du/dx
-1/(1+x^2 )
-v3/3

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