AP Calc Review - Danny & Madison

Question 1

Find the area of the region bounded by the parabolas y = x2 and y = 6x-x2.

Accepted Answer

9

Question 2

What is the limit of 3x2(2x-1) as x approaches -1/2

Accepted Answer

-3/2

Question 3

If f(x) = 2x3+4x2+7x+3

Accepted Answer

f'(2) = 35

Question 4

∫ln2x dx =

Accepted Answer

2xln2x-2x+c

Question 5

Find the linerization of f(x) = x + (1/x), when a = 1.

Accepted Answer

-0.567

Question 6

Given xy2=4, what is the second derivative of y = f(x) at the point (1,2)

Accepted Answer

1/2

Question 7

What is the instantaneous rate of change at t = -1 if f(t) = ((t3+t)/(4t+1))

Accepted Answer

-4/9

Question 8

A 20 foot ladder slides down a 10 feet wall at 5 ft/sec. What speed is the bottom sliding out.

Accepted Answer

2.887

Question 9

What is the relative maximum of the function y = x3+12x2+15x+3

Accepted Answer

-7.317

Question 10

Intergal of tan(x) from 0 to 1

Accepted Answer

ln(cos(1))

Question 11

dy/dx x2y+xy2 = 6

Accepted Answer

(2xy+y2)/(2xy+x2)

Question 12

What are the horizontal asymptotes for f(x) = ((5x)/(√x2+1))

Accepted Answer

y = 5 and y = -5

Question 13

d/dx tan2(4x) =

Accepted Answer

8*tan(4x)*sec(4x)

Question 14

limit of ((x2-25)/(x-5) as x approaches 5

Accepted Answer

10

Question 15

f(x) = 5x4/3, then f'(8) =

Accepted Answer

40/3

Questions 15