31.
$z_1=(\cos\frac{\pi}{16}+i\sin\frac{\pi}{16})^4=\cos\frac{\pi}{4}+i\sin\frac{\pi}{4}=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}i$
$z_2=2+i-\frac{\sqrt{2}}{\bar z_1}=2+i-\frac{\sqrt{2}}{\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i}$
$=2+i-\frac{2}{1-i}=2+i-(1+i)=1$
35.
$(f\circ g)(x)=\sqrt{3g(x)+1}=x^2+1\Rightarrow g(x)=\frac{1}{3}(x^2)(x^2+2)\Rightarrow g'(1)=\frac{4}{3}(1^3+1)=\frac{8}{3}$
$f'(x)=\frac{1}{2}(3x+1)^{-\frac{1}{2}}(3x+1)'\Rightarrow f'(1)=\frac{3}{2}(4^{-\frac{1}{2}})=\frac{3}{4}$
$f'(1)+g'(1)=\frac{8}{3}+\frac{3}{4}=\frac{41}{12}$
13 ¡Ã¡®Ò¤Á 2008, 22:01
