Let me process the text and equations from the image. I’ll extract the mathematical content and solve the problems provided. One moment, please. PIL import Image import pytesseract

Load the uploaded image

image_path = "/mnt/data/17333071067864kf7tm8e.jpg" image = Image.open(image_path)

Use OCR to extract text from the image

extracted_text = pytesseract.image_to_string(image) extracted_textThe OCR process didn't extract text properly from the image. Let me enhance the content or process it manually. One moment.From visual inspection of the image, the two main problems involve limits:

1. $\lim_{x \to 0} \left( x^2 + x \ln x \right) \frac{1}{x^2}$
2. $\lim_{x \to 0} \left( 1 + \tan^3 x \right) \frac{1}{x^3}$

I'll solve these problems step by step for you.

Problem 1:

$\lim_{x \to 0} \left( x^2 + x \ln x \right) \frac{1}{x^2}$

Rewrite the expression: $\lim_{x \to 0} \left( 1 + \frac{\ln x}{x} \right)$

Step 1: Simplify ( \frac{\ln x