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\( \lim _{x \rightarrow 0} \frac{x e^{x}-\sin x}{x} \) is equal to
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Verified Answer
The correct answer is:
\( 00 \)
Given that
\[
\begin{array}{l}
\lim _{x \rightarrow 0} \frac{x e^{x}-\sin x}{x}=\lim _{x \rightarrow 0}\left(\frac{x e^{x}}{x}-\frac{\sin x}{x}\right) \\
=\lim _{x \rightarrow 0} \frac{x e^{x}}{x}-\lim _{x \rightarrow 0} \frac{\sin x}{x} \\
=1-1=0
\end{array}
\]
\[
\begin{array}{l}
\lim _{x \rightarrow 0} \frac{x e^{x}-\sin x}{x}=\lim _{x \rightarrow 0}\left(\frac{x e^{x}}{x}-\frac{\sin x}{x}\right) \\
=\lim _{x \rightarrow 0} \frac{x e^{x}}{x}-\lim _{x \rightarrow 0} \frac{\sin x}{x} \\
=1-1=0
\end{array}
\]
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