Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Hello,

I need to evaluate the limits below but the grahp is made on paint, sorry about that.

1. lim x---> -3^+

2. lim x---> 0^-

3. lim x---> 0

4. lim x----> 6^+

The (^) means that the signs (+) or (-) are on top of the numbers.

Sorry if the graph is unreadable, thank you so much in advance!

The image presents a graph on a Cartesian coordinate system, illustrating a mathematical function. ### Components of the Graph: - **Axes**: - The horizontal line represents the x-axis, labeled as "X" on the positive side and "-X" on the negative side. - The vertical line represents the y-axis, labeled as "y" on the positive side and "-y" on the negative side. - **Graph of the Function**: - The graph is drawn in blue and represents the function \( f(x) \). - The curve shows fluctuations as it moves from left to right, indicating changes in the value of \( f(x) \) with respect to \( x \). - **Highlighted Points**: - Several points on the curve are marked with green circles, indicating key points or intersections. - Some points are larger, possibly indicating maximum or minimum values on the curve. - **Asymptote**: - A red dashed vertical line is present near \( x = 6 \), suggesting a vertical asymptote where the function approaches infinity. - **X-axis Overview**: - The negative side of the x-axis has points labeled from -4 to 0. - The positive side extends from 0 to 6. - **Y-axis Overview**: - The y-axis is labeled from -2 to 4, which captures the range of the function shown. ### Interpretation: - The graph depicts a polynomial or rational function with maximum and minimum values evident from the peaks and troughs. - The vertical asymptote indicates values where the function does not exist, typically representing division by zero in rational functions. - The function exhibits periodic behavior with apparent oscillations, which can be associated with certain trigonometric functions or other complex equations. This graph serves as a visual representation of function behavior, useful for analyzing continuity, limits, and points of interest such as extrema and asymptotic behavior.
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Transcribed Image Text:The image presents a graph on a Cartesian coordinate system, illustrating a mathematical function. ### Components of the Graph: - **Axes**: - The horizontal line represents the x-axis, labeled as "X" on the positive side and "-X" on the negative side. - The vertical line represents the y-axis, labeled as "y" on the positive side and "-y" on the negative side. - **Graph of the Function**: - The graph is drawn in blue and represents the function \( f(x) \). - The curve shows fluctuations as it moves from left to right, indicating changes in the value of \( f(x) \) with respect to \( x \). - **Highlighted Points**: - Several points on the curve are marked with green circles, indicating key points or intersections. - Some points are larger, possibly indicating maximum or minimum values on the curve. - **Asymptote**: - A red dashed vertical line is present near \( x = 6 \), suggesting a vertical asymptote where the function approaches infinity. - **X-axis Overview**: - The negative side of the x-axis has points labeled from -4 to 0. - The positive side extends from 0 to 6. - **Y-axis Overview**: - The y-axis is labeled from -2 to 4, which captures the range of the function shown. ### Interpretation: - The graph depicts a polynomial or rational function with maximum and minimum values evident from the peaks and troughs. - The vertical asymptote indicates values where the function does not exist, typically representing division by zero in rational functions. - The function exhibits periodic behavior with apparent oscillations, which can be associated with certain trigonometric functions or other complex equations. This graph serves as a visual representation of function behavior, useful for analyzing continuity, limits, and points of interest such as extrema and asymptotic behavior.
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