1. Limits and Continuity

Evaluate each limit. 

lim x→−1 (x^2−4+ 3√x^2−9)

Evaluate lim x→1 (x^3+3x^2−3x+1).

Suppose the rental cost for a snowboard is \$25 for the first day (or any part of the first day) plus \$15 for each additional day (or any part of a day).

Evaluate lim t→2.9 f(t).

Assume lim x→1 f(x)=8,lim x→1 g(x)=3, and lim x→1 h(x)=2 Compute the following limits and state the limit laws used to justify your computations.

lim x→1 (4f(x))

Assume lim x→1 f(x)=8,lim x→1 g(x)=3, and lim x→1 h(x)=2 Compute the following limits and state the limit laws used to justify your computations.

lim x→1 (f(x)−g(x))

Determine the following limits.

lim x→1000 18π^2

Determine the following limits.

lim x→1 √5x+6

Determine the following limits.

lim h→0 √5x + 5h − √5x / h, where x>0 Is constant

Determine the following limits.

lim h→0 (h + 6)^2 + (h + 6) − 42 / h

Suppose g(x) = {2x+1 if x≠0

5 if x=0.

Compute g(0) and lim x→0 g(x)

Determine the following limits.

lim x→a (3x + 1)^2 − (3a + 1)^2 / x − a, where a is constant

Suppose p and q are polynomials. If lim x→0 p(x) / q(x)=10 and q(0)=2, find p(0).

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→4(3x−7)

Determine the following limits.

lim x→3 1/ x − 3(1 /√x + 1 − 1/2)

Determine the following limits.

lim x→3 x^4 − 81 / x − 3