CHAPTER 2
Limits and Continuity SECTION 2.1 1.
The function f (x) is graphed. lim f (x) = x→0−
A. 0
B. 4
C. 2
D. undefined
2.
Answer true or false. For the function graphed lim f (x) is undefined. x→2
x2 − 9 x2 − 9 by evaluating f (x) = at x = 4, 3.5, 3.1, 3.01, 3.001, 2, 2.5, x→3 x − 3 x−3 2.9, 2.99, and 2.999.
3. Approximate the lim
B. −9
A. 6
D. −6
C. 0
4. Answer true or false. If lim f (x) = 6 and lim f (x) = 6, then lim f (x) = 0. x→0+
5. Approximate the A. 1
lim
x→−6−
x→0−
x x by evaluating f (x) = at appropriate values of x. x+6 x+6
B. 5
7. Approximate the limit by evaluating f (x) = A. 1
C. ∞
B. 0
6. Approximate the limit by evaluating f (x) = A. 1
x→0
D. −∞
5x 5x at appropriate values of x. lim− = sin x x→0 sin x 1 C. D. ∞ 5 sin x sin x at appropriate values of x. lim = x→0 x x
B. −1
C. 0 √
8. Approximate the limit by evaluating f (x) = √ x+1−1 lim = − x x→0 1 A. B. 0 2
x+1−1 at appropriate values of x. x
C. ∞
1
D. ∞
D. −∞