https://file.aiquickdraw.com/mathbot/file/1727213471638z5jas7oz.jpg

The image contains two limit problems regarding the functions \( f(x) \) and \( g(x) \), and we are tasked with evaluating these limits based on the graphs of these functions.

The problems are:

1. \( \lim_{x \to 2} [f(x) + g(x)] \)
2. \( \lim_{x \to 1} [f(x) + g(x)] \)

### Explanation of how to approach these problems:
1. **Interpretation of the given limits:**
   - For both (a) and (b), the task is to find the sum of the limits of the functions \( f(x) \) and \( g(x) \) as \( x \) approaches a certain value (2 in part (a) and 1 in part (b)).
   - Using the property of limits, \( \lim_{x \to a} [f(x) + g(x)] = \lim_{x \to a} f(x) + \lim_{x \to a} g(x) \), assuming the individual limits exist.

2. **Analyzing each limit:**
   - For part (a), we need to find:
     \[
     \lim_{x \to 2} f(x) + \lim_{x \to 2} g(x)
     \]
   - For part (b), we need to find:
     \[
     \lim_{x \to 1} f(x) + \lim_{x \to 1} g(x)
     \]

### Steps to solve:
- First, evaluate the individual limits \( \lim_{x \to a} f(x) \) and \( \lim_{x \to a} g(x) \) for both \( a = 2 \) and \( a = 1 \), by looking at the graphs of \( f(x) \) and \( g(x) \) (which were provided but are not visible in the image you uploaded).
- Once you find these individual limits, simply add them to get the required limits for each case.

Would you like to upload the graphs of \( f(x) \) and \( g(x) \) to proceed with solving this problem step by step? Let me know if you need further clarification!

Nos dan las gráficas de f y g. Úselas para evaluar cada límite si existe. Si el límite no existe, explique por qué.
(a) lim(x→2) [f(x) + g(x)]
(b) lim(x→1) [f(x) + g(x)]

Learn how to evaluate the limits of the sum of functions f(x) and g(x) as x approaches 2 and 1 using the graphs of f and g. The solution covers key concepts of limits and continuity, ideal for high school students studying calculus.

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