Explanation Derivative represents the instantaneous rate of change of one quantity with respect to another quantity. To find derivative of a functionf at x = a , we need to find the limit of the slope of secant line from x = a + h to x = a , as h tends to 0

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Concept explainers

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 3.1, Problem 1PS

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To describe the process of finding a derivative using the definition.

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Chapter 2, Problem 99SP

Chapter 3.1, Problem 2PS

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could you please show the computation of this by wires

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.

Chapter 3 Solutions

Calculus

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To describe the process of finding a derivative using the definition.

Solution Summary: The author describes the process of finding a derivative using the definition. Derivative represents the instantaneous rate of change of one quantity with respect to another quantity.

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Chapter 3 Solutions