Math / Calculus

QuestionConsider the limit $\lim _{x \rightarrow 0} \frac{\sin ^{2}(8 x)}{1-\cos (8 x)}$
To simplify this limit, we should multiply numerator and denominator by the expression $\square$ After doing this and simplifying the result we find that the value of limit is $\square$
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Studdy Solution
Now evaluate the limit as $x \rightarrow 0$ :
$\lim_{x \rightarrow 0} (1 + \cos(8x))$
Since $\cos(8x)$ approaches $\cos(0) = 1$ as $x \rightarrow 0$ , the limit is:
$1 + 1 = 2$
The expression to multiply by is:
$\boxed{1 + \cos(8x)}$
The value of the limit is:
$\boxed{2}$

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