Math Problem Statement

Evaluate the limit as x approaches 0 for (1 - cos(x)) / x^2.

Solution

It seems you've uploaded an image. Let me analyze it and extract the relevant details for you. PIL import Image

Load the uploaded image to examine it

img_path = '/mnt/data/17335366293400acy4lex.jpg' img = Image.open(img_path)

Display the image to analyze its contents

img.show()It looks like I can't display the image directly here, but I can analyze its contents. Let me process the image and extract any relevant text or details that can help with solving any related mathematical questions. pytesseract

Extract text from the image using OCR (Optical Character Recognition)

extracted_text = pytesseract.image_to_string(img)

extracted_textIt seems that no text was extracted from the image. This could be due to various factors like the image quality or the presence of non-text elements. If you can describe the image or upload a clearer version of it, I can help you with the mathematical details or questions related to it.

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Math Problem Analysis

Mathematical Concepts

Limits
Trigonometric Functions
Calculus

Formulas

1 - cos(x) ≈ x^2 / 2 as x → 0

Theorems

Taylor Expansion for Trigonometric Functions

Suitable Grade Level

Grades 11-12 or Introductory College Calculus