https://file.aiquickdraw.com/mathbot/file/1726746380881djnvcy4s.jpg

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:
   \[
  

Nilai limit lim(x→0) dari (4sin^2(2x))/(xtan(2x)) dan lim(x→π/4) dari (sin(x) - cos(x))/(tan(x) - 1)

This page provides a detailed step-by-step solution to two limit problems involving trigonometric functions. Learn how to apply L'Hopital's Rule and small-angle approximations to solve the limits lim(x→0) (4sin^2(2x))/(xtan(2x)) and lim(x→π/4) (sin(x) - cos(x))/(tan(x) - 1). Suitable for students in grades 11-12 studying pre-calculus or calculus.

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