AB Calculus Review

Derivatives

100

Find the derivative of 5x^2

10x

200

Find the derivative of ln(x^2)

What is (2x)/(x^2)

300

Find the derivative of (sinx)/(x^2)

(xcosx-2sinx)/(x^3)

400

f(x)=2e^.5x Find f'(x) and f''(x)

f'(x)=e^.5x f''(x)=.5e^.5x

500

x^2+y^2=25 at (0,5), find d^2y/dx^2

(-1/5)

Integrals

100

∫sinxdx

-cosx+C

200

∫x^5-4x^3dx from 0 to 2

(32/3)-16

300

∫(x(dx)/(1+4x^2)

(1/8)ln(1+4x^2)+C

400

∫(dy)/(1-y^2)^(1/2)

arcsin(y)+C

500

∫(e^x)/(1+e^2x)dx

arctan(e^x)+C

Limits

100

lim((x+2)(x-3))/(x^2+2x-15) as x approaches 3

5/8

200

lim as x approaches infinity (4-x^2)/((x^2)-1)

-1

300

lim as x approaches 0 of (sin5x)/x

5

400

lim as x approaches 0 of sin(1/x)

Does not exist

500

lim as x approaches infinity of (e^x)/(x^2)

Infinity

Related Rates

100

If a(t)=4t+1 and v(1)=3, then v(t) is

2t^2-t+2

200

A stone is thrown straight up from the top of a building with an initial velocity of 40 ft/sec and hits the ground 4 seconds later. What is the height of the building in feet?

96 feet

300

Solve for C in ydy=xdx

C=y^2-x^2

400

(dy/dx)=(x)/(9+x^2)^(1/2) If y=5 when x=4, solve for y

y=(9+x^2)^(1/2)

500

Solve if (dy/dx)=e^y and y=0 when x=1

-e^-y=x-2

Potluck

100

Find the derivative of 5x-8

5

200

The slope of the curve y^3-xy^2=4 at the point y=2 is

1/2

300

Find the area between the boundaries y=x^2,y=0,x=-1,and x=2

3

400

Find the area bounded by y=e^x, x=2, x=0 and the x-axis

(e^2)-1

500

What is Mrs. Lew's favorite color?

Yellow