© 2014 Shmoop University, Inc. All rights reserved.
Continuity of Functions

Continuity of Functions

Example 1

Let f(x) = 2x, c = 4, and ε = 0.5. Find an appropriate δ>0, as guaranteed by the continuity of f at 4.

Example 2

Let f(x) = x2, c = 2, and ε = 0.1. Find an appropriate value of δ>0 as guaranteed by the continuity of f at 2.

Example 3

Let f(x) = 4x + 1. 

Find a value of δ such that if |- 5| < δ, then |f(x) - f(5)| < 0.1.

Example 4

Let f(x) = sin(x

Find a value of δ such that if , then .

Example 5

Let  Find a value of δ such that if |x - 2| < δ, then |f(x) -0.5| < 0.005.

Example 6

Let . Find a value of δ such that if |x-7|<δ, then .

Advertisement
Advertisement
Advertisement