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- 1. Multiple Choice
A curve is defined by the parametric equations shown. What is d2y/dx2 ?
1 / (12et )
1 / ( 9et )
et / 2
3et / 4
- 2. Multiple Choice
–3 ln |x – 1| + 3 ln |x – 5| + C
–2 ln |x – 1| + 2 ln |x – 5| + C
3 ln |x – 1| – 3 ln |x – 5| + C
12 ln |x – 1| + 12 ln |x – 5| + C
- 3. Multiple Choice
The shaded region in the figure shown is bounded by the graphs of y = x2 – 1/4 and y = 1/16 – x4 for –½ ≤ x ≤ ½. Which of the following expressions gives the perimeter of the region?
A
B
C
D
- 4. Multiple Choice
The number of fish in a lake is modeled by the function P that satisfies the differential equation dP/dt = 0.003P(1000 – P), where t is the time in years. Which of the following could be the graph of y = P(t)?
A
B
C
D
- 5. Multiple Choice
Which of the following series is absolutely convergent?
A
B
C
D
- 6. Multiple Choice
Which of the following series cannot be shown to converge using the limit comparison test with the series shown.
A
B
C
D
- 7. Multiple Choice
The third-degree Taylor polynomial for the function f about x = 0 is T(x) = 3 – 4x + 2x2 – 3x3. Which of the following tables gives the values of f and its first three derivatives at x = 0?
A
B
C
D
- 8. Multiple Choice
What is the interval of convergence for the power series given?
–3 < x < 3
–3 < x ≤ 3
1 < x < 7
1 < x ≤ 7
- 9. Multiple Choice
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For time t ≥ 0 seconds, the position of an object traveling along a curve in the xy-plane is given by the parametric equations x(t) and y(t), where dx/dt = t2 + 3 and dy/dt = t3 + t. At what time t is the speed of the object 10 units per second?
1.675
1.813
4.217
10.191
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