Calculus AP Test Review

Limits

100

lim x→∞ (x+4)/(x^3-5x+2)

0 (BOBO)

200

lim x→∞ (6x^3 - 4x^2 + 5)/(2x^3 + 7x)

3 (EATS DC)

300

lim x→12 √(X+52)

8

400

lim x→0 (sinx)/(x)

1

500

Explain the Sum Rule

The limit of the sum of two functions is the sum of their limits

Continuity

100

f(x)=4 g(x)=7... Find f(x)-g(x)

-3

200

f(x)=5 g(x)=6 h(x)=3... Find h(x)*g(x)-f(x)

13

300

Is lim x→2 (x-2)/(x^2+4x-12) removable?

Yes

400

What are the conditions for continuity at x=a?

1. lim x→a exists 2. f(a) exists 3. lim x→a f(x)=f(a)

500

What are the two types of discontinuity and describe each of them

Removable discontinuity: You can reduce the the limit and remove the discontinuity Non-Removable Discontinuity: If you reduce the limit, you can not remove the discontinuity

Derivatives

100

7x-15

7

200

e^x - 7x

e^x - 7

300

lnx + 8x^3 - 5x^6

1/x +24x^2 -30x^5

400

csc(x)

-cscxcotx

500

arc cot(x)

-1/(1+x^2)

Antiderivatives

100

5x^4

x^5

200

7x^2-4x+3

7/3x^3-2x^2+3x

300

∫sinu du

-cosu+c

400

∫csc^2u du

-cotu + c

500

∫secu du

ln|secu+tanu|+c