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Exercise 103

Avg difficulty 2.5

Let f(t)f(t) be defined on 0≤t<10 \leq t < 1. Consider the average of the two extensions g(t)=Fodd(t)+Feven(t)2g(t) = \frac{F_{\text{odd}}(t)+ F_{\text{even}}(t)}{2}.

  1. What is g(t)g(t) if 0≤t<10 \leq t < 1 (Justify!)
  2. What is g(t)g(t) if −1<t<0-1 < t < 0 (Justify!)

Lebl, Notes on Diffy Qs, §4.4 Sine and cosine series, exercise 103

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Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.