Question

Помогите решить 3 5 7

Answer 1

$3)\; \; z=-i\; ,\; \; \; x+yi=0+(-1)i\\\\|z|=r=\sqrt{x^2+y^2}=\sqrt{0+1}=1\\\\x=rcos\phi =0\; ,\; \; cos\phi =0\; ,\\\\y=rsin\phi =-1\; ,\; \; sin\phi =-1\; \; \Rightarrow \; \; \phi =argz=-\frac{\pi}{2}\\\\-i=1\cdot (cos(-\frac{\pi}{2})+isin(-\frac{\pi}{2}))=cos(-\frac{\pi}{2})+isin(-\frac{\pi}{2})$

$5)\; \; y=(x^2-5x+8)^6\\\\y'=6\cdot (x^2-5x+8)^5\cdot (x^2-5x+8)'=6\cdot (x^2-5x+8)^5\cdot (2x-5)\\\\7)\; \; \int \frac{sin\sqrt[3]{x}}{\sqrt[3]{x^2}}\, dx=[t=\sqrt[3]{x}\; ,\; dt=-\frac{3dx}{2\sqrt[3]{x^2}}\, ]=-\frac{2}{3}\int sint\, dt=\\\\=-\frac{2}{3}\cdot (-cost)+C=\frac{2}{3}\cdot cos\sqrt[3]{x}+C$