Consider the function f(x)= cases x^ 2 -4 x-2 , & x<2

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Consider the function

f(x)=\begin{cases} \dfrac{x^{2}-4}{x-2}, & x<2,\\ ax+1, & x\ge 2. \end{cases}

For which value of

a

does

\displaystyle \lim_{x\to2} f(x)

exist? (a)

2

(b)

1

(c)

1.5

(d) There is no such value of

a