**Exercise 2.** Consider the functions $ g(x) $ and $ h(x) $ with the following graphs:**Graphs Overview:**1. **Graph of $ g(x) $ (Left Graph):** - The graph is composed of two line segments. - The segment for $ x < 0 $ is a horizontal line at $ y = 1 $, shown in green. - The segment for $ x > 0 $ is a horizontal line at $ y = -1 $, shown in blue. - At $ x = 0 $, there is an open circle at $ y = 1 $ and a filled circle at $ y = -1 $, indicating a discontinuity. The function value at $ x = 0 $ is $ g(0) = -1 $.2. **Graph of $ h(x) $ (Right Graph):** - The graph is also composed of two line segments. - The segment for $ x < 0 $ is a horizontal line at $ y = -1 $, shown in orange. - The segment for $ x > 0 $ is a horizontal line at $ y = 1 $, also shown in orange. - At $ x = 0 $, there is an open circle at $ y = -1 $ and a filled circle at $ y = 1 $, indicating a discontinuity. The function value at $ x = 0 $ is $ h(0) = 1 $.**Task:**Compute $ \lim_{x \to 0} (g(x) + h(x)) $.

Now, limx→0gx+hx=limx→0gx+limx→0hx

Answered: Exercise 2. Consider the functions g(x)…

Math

Calculus

Exercise 2. Consider the functions g(x) and h(x) with the following graphs: Compute lim(g(x)+ h(x)). x→0

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

**Exercise 2.** Consider the functions $ g(x) $ and $ h(x) $ with the following graphs:

**Graphs Overview:**

1. **Graph of $ g(x) $ (Left Graph):**
- The graph is composed of two line segments.
- The segment for $ x < 0 $ is a horizontal line at $ y = 1 $, shown in green.
- The segment for $ x > 0 $ is a horizontal line at $ y = -1 $, shown in blue.
- At $ x = 0 $, there is an open circle at $ y = 1 $ and a filled circle at $ y = -1 $, indicating a discontinuity. The function value at $ x = 0 $ is $ g(0) = -1 $.

2. **Graph of $ h(x) $ (Right Graph):**
- The graph is also composed of two line segments.
- The segment for $ x < 0 $ is a horizontal line at $ y = -1 $, shown in orange.
- The segment for $ x > 0 $ is a horizontal line at $ y = 1 $, also shown in orange.
- At $ x = 0 $, there is an open circle at $ y = -1 $ and a filled circle at $ y = 1 $, indicating a discontinuity. The function value at $ x = 0 $ is $ h(0) = 1 $.

**Task:**

Compute $ \lim_{x \to 0} (g(x) + h(x)) $.

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