Explanation Given information: The given relation is | f ( x ) − f ( y ) | < M | x − y | . Calculation: Consider the relation, | f ( x ) − f ( y ) | < M | x − y | Let c ∈ ( a , b ) then, | f ( x ) − f ( c ) | < M | x − c | Choosing δ = ∈ M , it is assumed that, 0 < | x

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 2, Problem 97SP

To determine

The proof that f is continuous at c .

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Chapter 2, Problem 96SP

Chapter 2, Problem 98SP

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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.

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Chapter 2 Solutions

Calculus

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The proof that f is continuous at c .

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Chapter 2 Solutions