Let's address the two limit problems visible in the image.

Problem 5:

$\lim_{x \to 0} \frac{4 \sin^2 (2x)}{x \tan (2x)}$

Solution:

To solve this, we will break it down step by step.

1. Use the small-angle approximations for sine and tangent when $x \to 0$:

   • $\sin(2x) \approx 2x$
   • $\tan(2x) \approx 2x$

2. Now, substitute these approximations into the expression: [