Calculus Review

Chapter 1

100

Find the limit of 2x-1, as it approaches 0.

-1

200

Find the limit of sinx as it approaches pi/2.

1

300

Find the limit of sqrt(x+1) as it approaches 3.

2

400

What is the limit as sinx goes to 5pi/6?

1/2

500

Find the limit of (x+3)^2 as it approaches -4.

1

Chapter 2

100

Find the derivative of F(x)=3x^2+4x-7.

F'(x)=6x+4

200

Find the derivative of F(x)=(1-cosx)/sinx.

-cscxcotx+csc^2x

300

find the derivative of F(x)=7/(3x^3).

F'(x)=7x^2

400

Find the derivative of F(x)=(2x-7)^3.

F'(x)=6(2x-7)

500

find dy/dx of x^2+y^2=36.

dy/dx=-x/y

Chapter 3

100

Find the critical numbers of F(x)=x^2(x-3).

x={0,2}

200

Find where F(x) is increasing, F(x)=x^2-6x.

F(x) is increasing on the interval (3, infinity)

300

Find the points of inflection of F(x)=x^3-6x^2+12x.

Points of inflection is (2,8)

400

Find all kinds of concavity of F(x)=3x^2-x^3.

concave up: (-infinity,1) concave down: (1,infinity)

500

Find the limit of (3x-2)/sqrt(2x^2+1) as x approaches infinity.

3/sqrt(2)

Chapter 4

100

Find the anti-derivative of 3x.

(3/2)x^2+C

200

Evaluate the summation when E i=1,n (i+1)/n^2, when n=10.

13/20

300

integrate sqrt(2x-1)dx.

1/3(2x-1)^(3/2)+C

400

Evaluate the integral from 0 to 3 of (x+2), using a geometric formula.

21/2

500

Evaluate the integral from 0 to 1 of x(x^2+1).

15/8

Chapter 5

100

differentiate F(x)=lnx(x^2+1)^2/sqrt(2x^3-1).

1/x+2(2x)/(x^2+1)-1/2(6x^2a)/(2x^3-1)

200

Differentiate F(x)=ln|cosx|.

-tanx

300

Integrate secxdx.

ln|secx+ tanx|+C

400

Integrate e^(3x+1)dx.

e^(3x+1)/3+C

500

Derive y=log(base10)cosx.

y'=-tanx/(ln10)