Question

4- Simplify the following expressions: 1-cos(t) a) 8(t) (2 points) t2 X4+1 b) Sex sin (re 171) (x – 1)dx (2 points)

The questions are posted above and the answers below them. I am unable to figure out how (1-cost)/t^2 becomes cost/2 in part a, and I do not understand why 1 is substituted into x for part b. Please help! Thank you.

Answer 1

of these We To understand the solution problems need to know Sampling propertus $ $(t) signal fCt>8Ct-t.) - fcto).8(t-to) cos(t) &Ct). a ) a t² 1 - cos (t) and to=o here f(t) +2 1- COS olo f (to=0) = Since foo is undefined form Lets find fro) by L-Hospitals Rule f(0) = Lt t to 1 - COSC) t2 LE tto contact-cost> d at (t2) sinco) It tyo 0+ sint 26 differentiate Numerator and denominator once

from LE pable (sint) txo (at) LE tyo cos (t> a COSCO from Hence fets &(t) fo&cts 1- COSCt) t2 I-cos (t) 8(t) = 38C) t² b) s ea sin (7 821) & (2-1) da - Šf (a) 8(2-1) dx f(x) 8(x-1) = f (12.862-1).

from a eesin (I xt1 2 f(1) = é sin(T. ) e sin (IT) -0. s f(x) &(8-1) dx. s f(1) 8 (2-3) dar od f(1) sos(x-1) da unit Area property of 8(a) is { $(X-26) dx =) facraobh : j e" sin (421) Sca-»da = fc forczuch oxl 11 s O