From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Functions, Graphs, and Limits

Functions, Graphs, and Limits

Graphing and Visualizing Limits Exercises

Example 1

Let y = f(x) = sin(x). What is the limit of f(x) as x approaches 0?

Example 2

Let y = f(x) = sin(x). What is the limit of f(x) as x approaches 2π?

Example 3

Let y = f(x) = sin(x). What is the limit of f(x) as x approaches π / 2?

Example 4

Let y = f(x) = sin(x). What is the limit of f(x) as x approaches -π?

Example 5

Let f(x) = x2 -4x + 3. Graph f(x) and use the graph to find the limit of f(x) as x approaches 0.

Example 6

Let f(x) = x2 -4x + 3. Graph f(x) and use the graph to find the limit of f(x) as x approaches 3.

Example 7

Let f(x) = x2 -4x + 3. Graph f(x) and use the graph to find the limit of f(x) as x approaches 1.

Example 8

Although we say "the limit of f(x) as x approaches 2 is 5," we write

limx → 2 f(x) = 5.

Let f(x) = 2 – 2x. Find the limit, limx → 2 f(x).

Example 9

Let f(x) = 2 – 2x. Find the limit, limx → 0 f(x).

Example 10

Let f(x) = 2 - 2x. Find the limit, limx → 1 f(x).

Advertisement