I see the mathematical problems written in the image. I will extract and solve the problems step-by-step. Let me process and provide solutions for them. It may take a moment to go through each one. PIL import Image import pytesseract

Load the image uploaded by the user

image_path = '/mnt/data/1733338395727btgdcdvm.jpg' image = Image.open(image_path)

Use OCR to extract text from the image

extracted_text = pytesseract.image_to_string(image)

Display the extracted text for verification

extracted_textThe OCR text extraction is not fully clear or accurate due to the handwritten nature of the mathematical problems. To address this, I will manually review the image and start solving the problems one by one based on my interpretation. Let’s begin with the first few limits and work systematically.### Solutions to the Problems

1. $\lim_{x \to 0} \frac{\sin x}{x}$

• Solution: This is a standard limit, and its value is $1$.

2. $\lim_{x \to 0} x^{-2}$

• As $x \to 0^+$, $x^{-2} = \frac{1}{x^2}$ approaches $+\infty$.
• Answer: $+\infty$.

3. $\lim_{x \to 0^+} 3$

• The value of a constant function is always the constant itself.
• Answer: $3$.

4. $\lim_{x \to \infty} \left(2x^2 - x \right)$

• The dominant term as $x \to \infty$ is $2x^2$.
• Answer: $+\infty$.

5. $\lim_{x \to 3} \sqrt{x^2 - 6x + 9}$

• Simplify the expression inside the square root: $\sqrt{x^2 - 6x + 9} = \sqrt{(x - 3)^2} = |x - 3|$
• As $x \to 3$, $|x - 3| \to 0$.
• Answer: $0$.

Would you like me to proceed with solving the next set of problems in the list? Let me know if you'd like further explanations or focus on any specific part!