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