The value of lim _{x rightarrow 0} frac{x e^{ | vedclass

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(C) We are given the limit: $\lim _{x \rightarrow 0} \frac{x e^{x}-\sin x}{x}$.By splitting the fraction,we get:$\lim _{x \rightarrow 0} \left( \frac{

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(C) We are given the limit: $\lim _{x \rightarrow 0} \frac{x e^{x}-\sin x}{x}$.By splitting the fraction,we get:$\lim _{x \rightarrow 0} \left( \frac{x e^{x}}{x} - \frac{\sin x}{x} \right)$$= \lim _{x \rightarrow 0} e^{x} - \lim _{x \rightarrow 0} \frac{\sin x}{x}$Using the standard limit $\lim _{x \rightarrow 0} \frac{\sin x}{x} = 1$ and evaluating $e^{0} = 1$:$= 1 - 1 = 0$.

The value of $\lim _{x \rightarrow 0} \frac{x e^{x}-\sin x}{x}$ is equal to:

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