Find: For the graph f(x) above, find: lim f(x) = -1- lim f(x) = 1114 lim f(x) = lim f(x) = 1-3 lim f(x) = 24-3+ lim f(x) = 24-3 -6 f(-1)= ƒ (-3) = -8- 9 -10-
Find: For the graph f(x) above, find: lim f(x) = -1- lim f(x) = 1114 lim f(x) = lim f(x) = 1-3 lim f(x) = 24-3+ lim f(x) = 24-3 -6 f(-1)= ƒ (-3) = -8- 9 -10-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcff5798b-7fe0-40b4-8b2c-b580bf1cfc79%2Ff54d297a-ec9c-44f6-af91-d598f41871d7%2F07ow0n_processed.jpeg&w=3840&q=75)
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.
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
Step 1: Description
Here, we have to find the limits at given points of f(x) by using given graph of f(x).
Step by step
Solved in 4 steps with 3 images
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