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Activity 3.2.2 .
Evaluate each of the following limits. If you use L’Hôpital’s Rule, indicate where it was used, and be certain the limit is indeterminate before you apply it.
(a)
\(\displaystyle \lim_{x \to 0} \frac{\ln(1 + x)}{x}\)
(b)
\(\displaystyle \lim_{x \to \pi} \frac{\cos(x)}{x}\)
(c)
\(\displaystyle \lim_{x \to 1} \frac{2 \ln(x)}{1-e^{x-1}}\)
(d)
\(\displaystyle \lim_{x \to 0} \frac{\sin(x) - x}{\cos(2x)-1}\)
