Answered: 2. (20 points) Let f be a periodic… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 35RE

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PLEASE ANSWER BOTH PARTS!!!

2. (20 points) Let f be a periodic function with period 2L for some L > 0. Suppose
f(x) -x for -L < x < L.
= ―
(a) (10 points) Sketch the graph of the given function for -3L ≤ x < 3L.
(b) (10 points) Find the Fourier series for f.

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. ^. 4 let f(x)=2x²-36x² + 20. Find the intervals where f is increasing. a) (-3,0) 0(3, ~) b) (-3,0) 0 (0,3) c) (-₁-3) 0 (0,3) d) (-0⁰0, -3) 0 (3₁ e) (0,3)0 (3,00)
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Number 16
Consider the sequence of functions {fn(x)} = {n²x(1 – x)"} for a E R and n = = 1,2, 3.... (a) Sketch on the same axis the graphs of f1(x) to f5(x).
Let f(x) = {1 { 2r, 0
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2. Which function is shown on the graph below? A. S(x) = tan-1/(x-7) - -2 B. /(x) = tan-1/(x+4)-2 c./(x)=-=tan(x-4)-2 D. S(x) = —tan (x + 1)-2 4 -3/2 - -1/2 f(x) 12
18
4. There is a function f that's continuous at 0 and /(x) = {(2x) for all x's please show that f must be a constant function. (1A.) Use induction to show that f(x) =f(2"x) for each integer n>0. (1B.) For a fixed x, how does 2"x behave for large integers n? (1C.) Using A. and B and the assumption about continuity, Explain why f(x)= f(0) for each x.
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