Evaluating limits without L'Hopital's I need to evaluate without using L'Hopital's Rule. They say you don't appreciate something until you lose it. Turns out to be true.


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*$\lim_{x \to 0} \frac{\sqrt[3]{1+x}-1}{x}$

*$\lim_{x \to 0} \frac{\cos 3x - \cos x}{x^2}$

I have tried to "rationalise" Q1 by using the identity $a^3-b^3=(a-b)(a^2+ab+b)$ but I still end up with a case of $\frac{0}{0}$.
For Q2, I tried to apply the formula and express $\cos 3x-\cos x =2\cos 2x \cos x$ which didn't help.
I would really be grateful for some advice on how I can proceed with the evaluating.

Q1 - good approach. But take $a=\sqrt[3]{1+x}$, $b=1$. See what happens. Not $\frac{0}{0}$.
Q2 - similarly - something should cancel and $\frac{0}{0}$ should vanish.
