I have problem evaluating limits with the variable in power, like the following limits:
- $\lim_{x \to 0} (1+ \sin 2x)^{\frac{1}{x}}$
- $\lim_{x \to \infty} \big(\frac{2x+5}{2x-1})^{2x}$
I asked the question like this to get the main idea behind evaluating these kind of limits, so I can solve all the related questions.