Explanation Given information: The function: f ( x ) = x + | x | Calculation: The graph of the function f ( x ) = x + | x | is shown in the figure. Zoom in toward the point ( − 1 , 0 ) Zooming in and in toward the point ( − 1 , 0 ) shows that the graph of f changes smoothly in the vicinity of this point

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

1st Edition

ISBN: 9781305779037

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 3.2, Problem 41E

To determine

To graph: f(x)=x+|x| . Zoom in repeatedly, first toward the point (−1,0) and then toward the origin. Also find difference about the behavior of f in the vicinity of these two points.

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Chapter 3.2, Problem 40E

Chapter 3.2, Problem 42E

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4 Consider f(x) periodic function with period 2, coinciding with (x) = -x on the interval [,0) and being the null function on the interval [0,7). The Fourier series of f: (A) does not converge in quadratic norm to f(x) on [−π,π] (B) is pointwise convergent to f(x) for every x = R П (C) is in the form - 4 ∞ +Σ ak cos(kx) + bk sin(kx), ak ‡0, bk ‡0 k=1 (D) is in the form ak cos(kx) + bk sin(kx), ak 0, bk 0 k=1

Solve the equation.

could you explain this please

Chapter 3 Solutions

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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To graph: f ( x ) = x + | x | . Zoom in repeatedly, first toward the point ( − 1 , 0 ) and then toward the origin. Also find difference about the behavior of f in the vicinity of these two points.

Solution Summary: The author illustrates how the graph of the function f(x)=x+sqrt left|x

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To graph: f(x)=x+|x| . Zoom in repeatedly, first toward the point (−1,0) and then toward the origin. Also find difference about the behavior of f in the vicinity of these two points.

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Chapter 3 Solutions