I=∮C2dzi(4z2+10z+4)=1i∮Cdz2z2+5z+2cap I equals contour integral over cap C of the fraction with numerator 2 space d z and denominator i open paren 4 z squared plus 10 z plus 4 close paren end-fraction equals 1 over i end-fraction contour integral over cap C of the fraction with numerator d z and denominator 2 z squared plus 5 z plus 2 end-fraction 4. Find the Poles
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By Cauchy's Residue Theorem, the integral along the closed contour is
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Res(f(z),−12)=12(−12+2)=12(32)=13Res open paren f of z comma negative one-half close paren equals the fraction with numerator 1 and denominator 2 open paren negative one-half plus 2 close paren end-fraction equals the fraction with numerator 1 and denominator 2 open paren three-halves close paren end-fraction equals one-third 7. Apply Cauchy's Residue Theorem
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follows a with mean 50 and variance 100. Find Q3. [20 Marks] a) Expand in a Laurent Series for the region
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