1. Limits and Continuity

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

Determine the following limits.

lim p→1 p^5 − 1 / p − 1

Determine the following limits.

lim x→5 x − 7 / x(x − 5)^2

Determine the following limits.

lim x→−5^+ x − 5 / x + 5

Determine the following limits.

lim x→3^- x − 4 / x^2 − 3x

Determine the following limits.

lim x→1^− x/ ln x

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

lim x→−95x

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

lim x→1(2x^3−3x^2+4x+5)

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

lim x→1 5x^2 + 6x + 1 / 8x − 4

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

lim p→2 3p / √4p + 1 − 1