1. Limits and Continuity

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

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

lim x→3 −5x / √4x − 3

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

lim x→2 (5x−6)^3/2

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

lim x→4 x^2 − 16 / 4 − x

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

lim x→b (x − b)^50 − x + b / x − b

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 − 1)^2 − 9 / x + 1

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

lim x→9 √x − 3 / x − 9

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

lim t→5 (1/t^2 − 4t − 5 −1/ 6(t − 5))

Let f(x) = {x^2+1 / if x<−1

√x+1 if x≥−1.

Compute the following limits or state that they do not exist.

limx→−1 f(x)

A right circular cylinder with a height of 10 cm and a surface area of S cm² has a radius given by r(S)=1/2(√100+2S/π −10).

Find lim S→0^+ r(S) and interpret your result.

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

lim x→1 x^2 − 1 / x − 1

Determine the following limits. 

lim x→∞ x^4+7 / x^5+x^2−x