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Connecting Infinite Limits and Vertical Asymptotes

Abigail Young

Abigail Young

7 min read

Study Guide Overview

This study guide covers the connection between infinite limits and vertical asymptotes. It reviews prerequisite knowledge of limits and introduces discontinuities, focusing on vertical asymptotes. The guide explains how to identify vertical asymptotes using infinite limits, provides examples and solutions, and offers practice questions with an answer key. Key topics include evaluating limits approaching infinity, identifying asymptotes from equations or graphs, and connecting function behavior near asymptotes to infinite limits.

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Question 1 of 11

Which of the following functions has a discontinuity at x=0x = 0?

f(x)=x2+2xf(x) = x^2 + 2x

g(x)=1x+1g(x) = \frac{1}{x+1}

h(x)=1xh(x) = \frac{1}{x}

k(x)=x+1k(x) = \sqrt{x+1}