1. Limits and Continuity

Limits and Continuity

In Exercises 5 and 6, find the value that lim (x→0) g(x) must have if the given limit statements hold.

lim ((4―g(x)) / x ) = 1

x→0

Limits and Continuity

In Exercises 5 and 6, find the value that lim (x→0) g(x) must have if the given limit statements hold.

lim (x lim g(x)) = 2

x→-4 x→0

Finding Limits

In Exercises 9–24, find the limit or explain why it does not exist.

lim x→a (x² ― a²)/(x⁴ ― a⁴)

Finding Limits

In Exercises 9–24, find the limit or explain why it does not exist.

lim h →0 ((x + h)² ― x²)/h

Finding Limits

In Exercises 9–24, find the limit or explain why it does not exist.

lim x →π sin (x/2 + sin x)

Finding Limits

In Exercises 9–24, find the limit or explain why it does not exist.

lim x →π cos² (x― tan x)

Suppose limx→c f(x) = 5 and lim x→c g(x) = −2. Find

b. limx→c 2f(x)g(x)

Calculating Limits

Find the limits in Exercises 11–22.

limt→6 8(t−5)(t−7)

Calculating Limits

Find the limits in Exercises 11–22.

limx→−1/2 4x(3x+4)²

Limits of quotients

Find the limits in Exercises 23–42.

limx→−5 (x² + 3x − 10) / x + 5

Limits of quotients

Find the limits in Exercises 23–42.

limx→−1 (√(x² + 8) − 3) / (x + 1)

Limits of quotients

Find the limits in Exercises 23–42.

limx→−3 (2 − √(x² − 5)) / (x + 3)

Limits with trigonometric functions

Find the limits in Exercises 43–50.

lim x→0 tan x

Limits with trigonometric functions

Find the limits in Exercises 43–50.

limx→−π √(x + 4) cos(x + π)

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

b. limx→b f(x)⋅g(x)