zuai-logo

Continuity

Emily Davis

Emily Davis

5 min read

Study Guide Overview

This guide covers jump discontinuities and essential discontinuities. Key concepts include the definition and properties of each discontinuity type, including how to identify them using left-hand and right-hand limits. The guide provides examples, practice questions, a glossary of terms, and exam strategies. It emphasizes that these discontinuities are not removable and often relate to sudden changes or infinite limits.

Question 1 of 7

Consider the function f(x)={2x+3if x<2x+8if x2f(x) = \begin{cases} 2x + 3 & \text{if } x < 2 \\ -x + 8 & \text{if } x \geq 2 \end{cases}. Does f(x)f(x) have a jump discontinuity at x=2x = 2?

Yes, because the left-hand limit is 7 and right-hand limit is 6

No, the function is continuous at x=2x=2

Yes, because the function is undefined at x=2x=2

No, because the left-hand limit is 6 and right-hand limit is 7