PIL import Image import pytesseract

Load the image to extract text

image_path = "/mnt/data/17326484071669bgoblua.jpg" extracted_text = pytesseract.image_to_string(Image.open(image_path))

extracted_textThe text from the image seems incomplete or unclear. Based on the mathematical context provided in the image, it appears to involve evaluating the limit:

$\lim_{(x, y) \to (0, 0)} \frac{5 - x^2}{4 + x + y}$

The result mentioned is $\frac{5}{4}$. Let me evaluate and verify it step-by-step:

Step 1: Evaluate the numerator and denominator as $(x, y) \to (0, 0)$.

• Numerator: $5 - x^2 \to 5 - 0^2 = 5$.
• Denominator: $4 + x + y \to 4 + 0 + 0 = 4$.

Step 2: Combine the results.

$\lim_{(x, y) \to (0, 0)} \frac{5 - x^2}{4 + x + y} = \frac{5}{4}$

Thus, the answer is indeed correct: $\frac{5}{4}$.

Would you like further clarifications or details? Here are some related questions to deepen understanding:

1. Why does substituting $(x, y) \to (0, 0)$ directly work in this case?
2. How do we deal with indeterminate forms when limits cannot be directly evaluated?
3. What would happen if the denominator approached 0?
4. How do partial derivatives relate to limit evaluations in multivariable calculus?
5. Can this limit be evaluated along different paths to verify the result?

Tip: Always check for path dependency in multivariable limits to ensure the result is independent of the approach direction.