(3) $\lim _{x \rightarrow a} \frac{\sin x-\sin a}{x-a}$;

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∻Solution by Steps∻ ‖ step 1 ⋮ Apply L'Hôpital's Rule since the limit is of the indeterminate form $\frac{0}{0}$. ‖ ‖ step 2 ⋮ Differentiate the numerator and the denominator with respect to $x$. ‖ ‖ step 3 ⋮ The derivative of $\sin(x)$ is $\cos(x)$, and the derivative of $x$ is $1$. ‖ ‖ step 4 ⋮ Substitute $x$ with $a$ in the derivative of the numerator. ‖ ‖ step 5 ⋮ The limit becomes $\lim_{x o a} \frac{\cos(x)}{1} = \cos(a)$. ‖ ∻Answer∻ ⚹ $\cos(a)$ ⚹ ∻Key Concept∻ ⚹L'Hôpital's Rule for Indeterminate Forms⚹ ∻Explanation∻ ⚹When faced with a limit that results in an indeterminate form such as $\frac{0}{0}$, L'Hôpital's Rule can be applied by taking the derivative of the numerator and the denominator separately and then evaluating the limit.⚹◊What is the formula for finding the limit of $ \lim_{x ightarrow a} \frac{\sin x - \sin a}{x - a} $?⍭ Generate me a similar question◊

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