Mathematics

Problem

A function

h

is defined by

h(x)=\begin{cases} \sqrt{9-4x^{2}}, & -\dfrac{3}{2}\le x<1,\\ |x-1|, & x\ge1. \end{cases}

Answer the following: a. (i) Evaluate the left-hand limit of

h(x)

x

approaches

1

from values less than

1

. b. (ii) Evaluate the right-hand limit of

h(x)

x

approaches

1

from values greater than

1

. c. (iii) Hence decide whether

\displaystyle\lim_{x\to1}h(x)

exists and, if it exists, find its value.