Mathematics

Problem

Let

F(x)=\begin{cases} \dfrac{x^2-1}{x-1}, & x\neq1,\\ m, & x=1. \end{cases}

The constant

m

is a real number. a. Part 1: (a) Describe the type of discontinuity that

F

exhibits at

x=1

when

m\neq2

. Support your description with appropriate reasoning. b. Part 2: (b) Determine the value of

m

that eliminates the discontinuity at

x=1

, and justify your result analytically. c. Part 3: (c) For the value of

m

found in part (b), classify the continuity of

F

x=1

and explain why the classification holds.