Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why. $\lim _{x \rightarrow 0} \frac{\sqrt{1+2 x}-\sqrt{1-4 x}}{x}$
Added by Jared B.
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However, we cannot apply l'Hospital's Rule directly because the functions in the numerator and denominator are not differentiable at $x=0$. Instead, we can use a more elementary method by rationalizing the numerator. We have: $$\lim_{x \rightarrow 0} Show more…
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