Find (a) $\lim_{x \to 0} \frac{\sqrt{1 + \tan(x)} - \sqrt{1 + \sin(x)}}{x^3}$ (b) $\lim_{x \to 0} \frac{d^4}{dx^4} \left( \frac{\sin(x)}{x} \right)^3$
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For the first limit, we have \[ \lim_{r \to \tan^{-1}(1)} \frac{1}{\sin(\pi)} = \frac{1}{\sin(\pi)} = \frac{1}{0} \] Since the denominator is zero, the limit does not exist. Show moreβ¦
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