AP Calculus BC Total Review

A curve is defined by the parametric equations shown. What is ? $\frac{d^2y}{dx^2}$  ?

• 1 / (12e^t )

• 1 / ( 9e^t )

• e^t / 2

• 3e^t / 4

• –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

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

The shaded region in the figure shown is bounded by the graphs of  $y=x^2-\frac{1}{4}$ and  $y=\frac{1}{16}-x^4$   for  $-\frac{1}{2}≤\ x\ ≤\ \frac{1}{2}$ . Which of the following expressions gives the perimeter of the region?

• A

• B

• C

• D

Tags

CCSS.HSA.REI.C.7

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

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Which of the following series is absolutely convergent?

• A

• B

• C

• D

Which of the following series cannot be shown to converge using the limit comparison test with the series shown.

• A

• B

• C

• D

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

Tags

CCSS.HSA.APR.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the interval of convergence for the power series given?

• –3 < x < 3

• –3 < x ≤ 3

• 1 < x < 7

• 1 < x ≤ 7

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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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1