Question

ребята, решите, пожалуйста ! ))

Answer 1

1)
$y=-ctg2x \ y=frac{ctg^{2}x-1}{2ctgx} \ ctg^{2}x-1=0geq 0 \ ctg^{2}xgeq 1 \ ctgx=1 \ 2ctgxneq 0 \ ctgxneq 0 x=(0;1]$

2)
$y=frac{1}{sqrt{2x-1}} \ intlimits{frac{1}{sqrt{2x-1}}= intlimits{frac{1}{sqrt{4(frac{2x}{4}-frac{`1}{4})}}dy= intlimits{frac{1}{2sqrt{frac{2x}{4}-frac{1}{4}}}= frac{1}{2}intlimits{frac{1}{sqrt{frac{2x}{4}-frac{1}{4}}} \ frac{1}{2}arcsinfrac{2x}{sqrt{2x}}+C$

3)
$x_{0}=0 \ y_{0}=2 \ y=5x-frac{5}{3}x^{3} \ x=0 y=0 \ y=2 \ 5x-frac{5x^{3}}{3}=2 \ 15x-5x^{3}=6 \ 5x(3x-x^{2})=6 \ 5x=6 \ x=1.2 \ 3x-x^{2}=6 \ x^{2}-3x+6=0 \ x_{1,2}neq 0$
x=1.2