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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