Xe and x, denote the even and odd parts of x,

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I need help solving 3.11
/Users/Lenovo/Desktop/signals&systems/signals_and systems-3.0.pdf
+1
JA
where A is a positive real constant.
3.11 Show that, for any function x,
roo
where
Xe
and x, denote the even and odd parts of x, respectively.
3.12 Let x denote a function with derivative y.
(a) Show that if x is even then y is odd.
(b) Show that if x is odd then y is even.
3.13 For an arbitrary function x with even and odd parts Ne and x., respectively, show that:
(a) Xe(1)Xo(1)dt = 0; and
(b) x(1)dt=te(1)dt.
3.14 Show that:
Transcribed Image Text:/Users/Lenovo/Desktop/signals&systems/signals_and systems-3.0.pdf +1 JA where A is a positive real constant. 3.11 Show that, for any function x, roo where Xe and x, denote the even and odd parts of x, respectively. 3.12 Let x denote a function with derivative y. (a) Show that if x is even then y is odd. (b) Show that if x is odd then y is even. 3.13 For an arbitrary function x with even and odd parts Ne and x., respectively, show that: (a) Xe(1)Xo(1)dt = 0; and (b) x(1)dt=te(1)dt. 3.14 Show that:
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