Mathematics

Problem

A function f is defined as

f(x)=\begin{cases} \dfrac{x^2-1}{x-1}, & x\neq 1,\\ c, & x=1. \end{cases}

Answer the following questions about the behavior of f at

x=1

. a. Part 1: (a) Evaluate

\displaystyle\lim_{x\to 1}f(x)

algebraically. b. Part 2: (b) Determine the value of the constant

c

that makes

f

continuous at

x=1

. Show your work. c. Part 3: (c) Describe, using appropriate limit terminology, why the discontinuity of

f

x=1

is classified as removable once the value of

c

found in part (b) is assigned.