Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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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 topic…
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Using the graph, find each limit or explain why the limit does not exist. a. lim x-> -1f(x) b. lim x -> 1f(x) c. lim x -> 0+f(x) d. lim x -> 2f(x) 

**Graph Explanation: Piecewise Function** This diagram illustrates a piecewise function on a coordinate plane. Here’s a detailed breakdown of each component of the graph: ### Axes and Scale: - **X-Axis (Horizontal):** The x-axis ranges from -2 to 2. - **Y-Axis (Vertical):** The y-axis ranges from -2 to 4. - Both axes intersect at the origin (0,0). ### Graph Description: 1. **Left Segment:** - A curve begins from the top-left and moves downward, approaching the point (-1, 1). - There is an open circle at (-1, 1) indicating that this point is not included in the function. 2. **Vertical Section:** - The graph exhibits a vertical movement from the open circle at (-1, 1) downwards, connecting to the negative region of the y-axis at around (0, -1). - An open circle is present at the origin (0, 0), denoting the exclusion of this point. 3. **Right Segment:** - From the open circle at the origin, a new curve emerges moving upward to the right. - The curve includes an open circle at the point (1, 1). 4. **Isolated Point:** - A filled black circle is plotted at (1, -1), representing a specific inclusion of this point in the function. ### Summary: This graph clearly illustrates a piecewise function with specific intervals and defined points. The open circles denote points not included in the function on those segments, while the filled black circle at (1, -1) emphasizes its inclusion at that coordinate.
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Transcribed Image Text:**Graph Explanation: Piecewise Function** This diagram illustrates a piecewise function on a coordinate plane. Here’s a detailed breakdown of each component of the graph: ### Axes and Scale: - **X-Axis (Horizontal):** The x-axis ranges from -2 to 2. - **Y-Axis (Vertical):** The y-axis ranges from -2 to 4. - Both axes intersect at the origin (0,0). ### Graph Description: 1. **Left Segment:** - A curve begins from the top-left and moves downward, approaching the point (-1, 1). - There is an open circle at (-1, 1) indicating that this point is not included in the function. 2. **Vertical Section:** - The graph exhibits a vertical movement from the open circle at (-1, 1) downwards, connecting to the negative region of the y-axis at around (0, -1). - An open circle is present at the origin (0, 0), denoting the exclusion of this point. 3. **Right Segment:** - From the open circle at the origin, a new curve emerges moving upward to the right. - The curve includes an open circle at the point (1, 1). 4. **Isolated Point:** - A filled black circle is plotted at (1, -1), representing a specific inclusion of this point in the function. ### Summary: This graph clearly illustrates a piecewise function with specific intervals and defined points. The open circles denote points not included in the function on those segments, while the filled black circle at (1, -1) emphasizes its inclusion at that coordinate.
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