1. Limits and Continuity

Use Theorem 3.10 to evaluate the following limits.

lim x🠂0 (sin 7x) / 3x

Limits of quotients

Find the limits in Exercises 23–42.

limx→−5 (x² + 3x − 10) / x + 5

Find the limits in Exercises 53–58. Write ∞ or −∞ where appropriate.

lim (x² − 3x + 2) / (x³ − 2x²) as

d. x→2

10. True, or false? As x→∞,

a. 1/(x+3) = O(1/x)

Suppose limx→b f(x) = 7 and lim x→b g(x) = −3. Find

b. limx→b f(x)⋅g(x)

Determine the following limits.

b. $\underset{x\to 3}{\lim }\frac{x-3}{x^4-9x^2}$

Suppose g(x) = {x^2−5x if x≤−1

ax^3−7 if x>−1.

Determine a value of the constant a for which lim x→−1 g(x) exists and state the value of the limit, if possible.