Answer
\[ - 1\]
Work Step by Step
\[\begin{gathered}
\mathop {\lim }\limits_{x \to 0} \frac{{1 - {e^x}}}{x} \hfill \\
{\text{Evaluate }}f\left( x \right){\text{ for the given values and complete the table}}{\text{.}} \hfill \\
x = - 0.1 \to f\left( { - 0.1} \right) = \frac{{1 - {e^{ - 0.1}}}}{{ - 0.1}} \approx - 0.9516 \hfill \\
x = - 0.01 \to f\left( { - 0.01} \right) = \frac{{1 - {e^{ - 0.01}}}}{{ - 0.01}} \approx - 0.9950 \hfill \\
x = - 0.001 \to f\left( { - 0.001} \right) = \frac{{1 - {e^{ - 0.001}}}}{{ - 0.001}} \approx - 0.9995 \hfill \\
x = 0.001 \to f\left( {0.001} \right) = \frac{{1 - {e^{0.001}}}}{{0.001}} \approx - 1.0005 \hfill \\
x = 0.01 \to f\left( {0.01} \right) = \frac{{1 - {e^{0.01}}}}{{0.01}} \approx - 1.0050 \hfill \\
x = 0.1 \to f\left( {0.1} \right) = \frac{{1 - {e^{0.1}}}}{{0.1}} \approx - 1.0517 \hfill \\
\boxed{\begin{array}{*{20}{c}}
x&{f\left( x \right)} \\
{ - 0.1}&{ - 0.9516} \\
{ - 0.01}&{ - 0.9950} \\
{ - 0.001}&{ - 0.9995} \\
{0.001}&{ - 1.0005} \\
{0.01}&{ - 1.0050} \\
{0.1}&{ - 1.0517}
\end{array}} \hfill \\
{\text{Therefore,}} \hfill \\
\mathop {\lim }\limits_{x \to 0} \frac{{1 - {e^x}}}{x} \approx - 1 \hfill \\
{\text{Graph}} \hfill \\
\end{gathered} \]
