ANSWERS – BC CALCULUS TAKE-HOME MULTIPLE CHOICE TEST - ANSWERS PART A – NO CALCULATOR ALLOWED

1. B

2. A

3. = C

4. Ratio Test D

5. and C

6. A I. f has a limit at x = 2. True II. f is continuous at x = 2. False III. f is differentiable at x = 2. False

f is not continuous, so f is not differentiable

7. Given that and what is the approximation for y(2) if Euler’s method is used with a

step size of 0.5, starting at x = 1?

D 8. Left Riemann Sum:

B

ANSWERS – BC CALCULUS TAKE-HOME MULTIPLE CHOICE TEST - ANSWERS

9. . This occurs at x = 1.

So, g(1) is greatest, as shown by the graph. D

Graph of f

10.

11. R is the region between and x-axis,

A

12. Ratio Test

Therefore, Converges D

13. B

14. The graph of f changes concavity in (0,2) because the second derivative goes from positive to negative on

this interval. E

15. , A

ANSWERS – BC CALCULUS TAKE-HOME MULTIPLE CHOICE TEST - ANSWERS

16. Geometric Series only D

17. B 18. line

So, A

19. Cover-Up Method

When When

A

20.

If C

21. Velocity of particle increasing graph of is concave up when A

22. Integration by parts:

23. E

ANSWERS – BC CALCULUS TAKE-HOME MULTIPLE CHOICE TEST - ANSWERS

24.

Using the following model formula for

logistic growth: dPdt

= kP( A− P)

dPdt

= kP( A− P) = kP(200 − P) = k(200P − P2 )

Only one of the 5 choices can be put

into the form dPdt

= k(200P − P2 ) :

dPdt

= .2P − .001P2 = .001(200P − P2 ) → k = .001

Carrying Capacity = A = 200

A

25.

So, B 26. when = 0 and

D

27. Look at graph A

28. Speed =

plug x = 2

So, D

y -2 -1 0 1 2 3 0 -1 0 3

ANSWERS – BC CALCULUS TAKE-HOME MULTIPLE CHOICE TEST - ANSWERS PART B – CALCULATOR ALLOWED

76. 1st derivative test 2nd derivative test Point of inflection at = D

77. D

78. ok ok ok ok -2 and 0 only C

79. If converges to k, by the integral test, converges D

80.

graph using your calculator - it changes signs (crosses x-axis) 5 times from (-2 to 2) E

81. (P-Q)-(R-S)= P-Q-R+S B

82. If diverges and for all n, which is true? By the direct comparison test, diverges E

83. What is area enclosed by and

B

84. A

85. The graph of on changes signs twice C

86.

C

ANSWERS – BC CALCULUS TAKE-HOME MULTIPLE CHOICE TEST - ANSWERS

87. D

88.

Since

and

89. No c, for which

Therefore, Rolle’s Therom is violated. So f not continuous, which implies not differentiable. does not exist. E 90. D

91. ,

The graph of from positive to negative at D

92.