BC Calculus AP Prep

A curve is defined by the parametric equations shown. What is d²y/dx² ?

• 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 = 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

Which of the following series is absolutely convergent?

• 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

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

• –3 < x < 3

• –3 < x ≤ 3

• 1 < x < 7

• 1 < x ≤ 7

Calculator Active:

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

What is the answer to this problem?

• A

• B

• C

• D

• E

For t≥0, a particle moving in the xy-plane has velocity v(t) = <5e^-t, sin(1+t)>. What's the total distance the particle traveled from 0 ≤ t ≤ 2? (Calc. Active)

• 1.861 meters

• 2.236 meters

• 1.695 meters

• 4.613 meters

For x(t) = 3t²-3, y(t) = 2t +1, find the slope of the tangent at t = 1

• 1/3

• 1

• 2

• 3