1. Limits and Continuity

Graph the function f(x)=e^−x / x(x+2)^2 using a graphing utility. (Experiment with your choice of a graphing window.) Use your graph to determine the following limits.

b. lim x→−2 f(x)

Graph the function f(x)=e^−x / x(x+2)^2 using a graphing utility. (Experiment with your choice of a graphing window.) Use your graph to determine the following limits.

d. lim x→0^+ f(x)

Graph the function f(x)=e^−x / x(x+2)^2 using a graphing utility. (Experiment with your choice of a graphing window.) Use your graph to determine the following limits.

c. lim x→0^− f(x)

Suppose f(x)→100 and g(x)→0, with g(x)<0 as x→2. Determine lim x→2 f(x) / g(x).

Which of the following statements are correct? Choose all that apply.

a. lim x→1 1/ (x−1)^2 does not exist

b. lim x→1 1/ (x−1)^2=∞

c. lim x→1 1/(x−1)^2=−∞

Determine the following limits.

a. lim x→2^+ 1 x − 2

Determine the following limits.

b. lim x→3^− 2/(x − 3)^3

Determine the following limits.

a. lim x→4^+ x − 5 / (x − 4)^2

Determine the following limits.

b. lim x→4^− x − 5 / (x − 4)^2

Determine the following limits.

c. lim x→4 x − 5 / (x − 4)^2

Determine the following limits.

a. lim x→1^+ x / |x − 1|

Determine the following limits.

c. lim x→1 x / |x − 1|

Determine the following limits.

a. lim z→3^+ (z − 1)(z − 2) / (z − 3)

The graph of ℎ in the figure has vertical asymptotes at x=−2 and x=3. Analyze the following limits. <IMAGE>

lim x→−2 h(x)

Determine the following limits.

a. lim x→−2^+ (x − 4) / x(x + 2)