Let $f(x)=\begin{cases} e^{1/x}, & x<0,\\ k, & x=0,\\ \ln(1+x), & x>0. \end{cases}$ …

Mathematics

Problem

Let

f(x)=\begin{cases} e^{1/x}, & x<0,\\ k, & x=0,\\ \ln(1+x), & x>0. \end{cases}

Determine the value of

k

that makes

f

continuous at

x=0