The function is defined by f(x)= cases e^ kx , & x<0, 1+x, & x 0

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The function

f

is defined by

f(x)=\begin{cases}e^{kx}, & x<0,\\1+x, & x\ge 0.\end{cases}

Determine the value of the constant

k

for which

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

exists.