Let be the function defined by g(x)= cases e^ x -1 x , & x0

MATHEMATICS · Single correct · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

Let

g

be the function defined by

g(x)= \begin{cases} \dfrac{e^{x}-1}{x}, & x<0,\\ \dfrac{\ln(1+ax)}{x}, & x>0. \end{cases}

For which value of the constant

a

does

\displaystyle\lim_{x\to 0} g(x)

exist? (a)

a=e

(b)

a=0

(c)

a=1

(d)

a=\dfrac{1}{e}