Mathematics

Mathematics

Problem

Define the function

h:\mathbb R\to\mathbb R

by

h(x)=\begin{cases}\displaystyle\frac{x^{2}-4}{x-2}, & x\neq2,\;x\neq-2,\\[4pt]k, & x=2,\\[4pt]m, & x=-2.\end{cases}

Answer the following questions. a. (i) Find

\displaystyle\lim_{x\to2}\frac{x^{2}-4}{x-2}

. b. (ii) Find

\displaystyle\lim_{x\to-2}\frac{x^{2}-4}{x-2}

. c. (iii) Determine the values of

k

and

m

that make

h

continuous at both

x=2

and

x=-2

. d. (iv) State the final continuous form of

h(x)

incorporating the values of

k

and

m

obtained above.

Browse the problem library