mathop {lim }limits_{x to 0} frac{sin x}{x} i | vedclass

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(A) The limit $\mathop {\lim }\limits_{x 	o 0} \frac{\sin x}{x}$ is a standard limit in calculus.By using the Taylor series expansion for $\sin x$,we

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$1$

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(A) The limit $\mathop {\lim }\limits_{x 	o 0} \frac{\sin x}{x}$ is a standard limit in calculus.By using the Taylor series expansion for $\sin x$,we have $\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \dots$Therefore,$\frac{\sin x}{x} = \frac{x - \frac{x^3}{6} + \dots}{x} = 1 - \frac{x^2}{6} + \dots$As $x 	o 0$,the expression approaches $1$.

$\mathop {\lim }\limits_{x \to 0} \frac{\sin x}{x}$ is equal to

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