What is mean by Even function and Odd function, explain by example, Identify the given function, explain the nature of the given function, If f(x) be a function of period 2n such that, -π<00 f(x) = {x, 0

What is mean by Even function and Odd function, explain by example, Identify the given function, explain the nature of the given function, If f(x) be a function of period 2n such that, -π<00 f(x) = {x, 0

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.6: Transformations Of Functions

Problem 104E

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Concept explainers

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 topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

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What is mean by Even function and Odd function, explain by example, Identify the
given function, explain the nature of the given function, If f(x) be a function of period
2n such that,
-π<00
f(x) = {x,
0 <x <T
(a) Sketch a graph of f(x) in the interval -3n<x< 3n.
(b) Show that the Fourier series for f(x) in the interval a<x<n is
1
-= cosx +z cos3x + 7 cos5x +
1
32
...
.....
4
(c) By giving appropriate values to x, show that
! = -
(1)
.....
5
7
1
1
(ii)
= 1+
32
..... ...
52

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