Let and . (i) Simplify and wherever they are defined. (ii) Obtain the simplified…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x)=\frac{x^{2}-4}{x-2}

and

g(x)=\frac{3x-6}{x-2}

. (i) Simplify

f(x)

and

g(x)

wherever they are defined. (ii) Obtain the simplified expression for

(f+g)(x)

and state its domain. (iii) Explain why the limit

\displaystyle \lim_{x\to 2}(f+g)(x)

exists even though neither

f

nor

g

is defined at

x=2

, and find its value.