Mathematics

Problem

Consider the function

f(x)=\begin{cases} \dfrac{x^2-4}{x-2}, & x<2,\\ mx+n, & x\ge 2. \end{cases}

where

m

and

n

are real constants. a. Part 1: (a) Determine the limit of

f(x)

x

approaches

2

from the left. b. Part 2: (b) Determine the limit of

f(x)

x

approaches

2

from the right in terms of

m

and

n

. c. Part 3: (c) Find all values of

m

and

n

that make

f

continuous on the entire real line. d. Part 4: (d) State every maximal open interval on which the resulting continuous function is differentiable and justify your answer.

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