Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
For the graph \( f(x) \) above, find:

Find:

\[ \lim_{{x \to 1^-}} f(x) = \]

\[ \lim_{{x \to 1^+}} f(x) = \]

\[ \lim_{{x \to 1}} f(x) = \]

\[ \lim_{{x \to 3^-}} f(x) = \]

\[ \lim_{{x \to 3^+}} f(x) = \]

\[ \lim_{{x \to 3}} f(x) = \]

\[ f(-1) = \]

\[ f(-3) = \]

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Explanation of Graph:

- The graph is a curve depicted on a coordinate plane.
- The y-axis ranges from -10 to 5, while the x-axis is not labeled with specific numbers, but notable points appear to be at integer values.
- Key points marked on the graph include open circles, indicating points where the function is not defined.
- One of the open circles is at the point (3, -3), and another at (-3, -5).
- The curve passes through different quadrants, showing distinct changes in direction indicating local maxima and minima.
- The graph is continuous except at the open circles where there might be jumps or holes in the function.
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Transcribed Image Text:For the graph \( f(x) \) above, find: Find: \[ \lim_{{x \to 1^-}} f(x) = \] \[ \lim_{{x \to 1^+}} f(x) = \] \[ \lim_{{x \to 1}} f(x) = \] \[ \lim_{{x \to 3^-}} f(x) = \] \[ \lim_{{x \to 3^+}} f(x) = \] \[ \lim_{{x \to 3}} f(x) = \] \[ f(-1) = \] \[ f(-3) = \] [Submit Button] Explanation of Graph: - The graph is a curve depicted on a coordinate plane. - The y-axis ranges from -10 to 5, while the x-axis is not labeled with specific numbers, but notable points appear to be at integer values. - Key points marked on the graph include open circles, indicating points where the function is not defined. - One of the open circles is at the point (3, -3), and another at (-3, -5). - The curve passes through different quadrants, showing distinct changes in direction indicating local maxima and minima. - The graph is continuous except at the open circles where there might be jumps or holes in the function.
The image shows a graph on a coordinate plane with a blue quadratic curve passing through the points. The x-axis and y-axis range from -10 to 10. Here is a detailed description of the graph and its components:

1. **Quadratic Curve**: The blue curve represents a quadratic function (parabola) that opens upward.

2. **Axes**: 
   - The x-axis and y-axis are marked at intervals from -10 to 10.
   - The intersection at the origin (0,0) is shown.

3. **Red Points**:
   - Four red points are plotted on the graph.
   - They are located at (-3, -3), (-1, -5), (0, -6), and (2, -3).

4. **Grid Lines**:
   - The graph is drawn on a grid with equal intervals, providing a clear background to locate points.

This graph visually represents the behavior of a quadratic function and highlights specific plotted points for analysis or educational purposes.
expand button
Transcribed Image Text:The image shows a graph on a coordinate plane with a blue quadratic curve passing through the points. The x-axis and y-axis range from -10 to 10. Here is a detailed description of the graph and its components: 1. **Quadratic Curve**: The blue curve represents a quadratic function (parabola) that opens upward. 2. **Axes**: - The x-axis and y-axis are marked at intervals from -10 to 10. - The intersection at the origin (0,0) is shown. 3. **Red Points**: - Four red points are plotted on the graph. - They are located at (-3, -3), (-1, -5), (0, -6), and (2, -3). 4. **Grid Lines**: - The graph is drawn on a grid with equal intervals, providing a clear background to locate points. This graph visually represents the behavior of a quadratic function and highlights specific plotted points for analysis or educational purposes.
Expert Solution
Check Mark
Step 1: Description

Here, we have to find the limits at given points of f(x) by using given graph of f(x).

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