Question

Answer 1

\(x.f'\left(x\right)+f^2\left(x\right)=f\left(x\right)\)

\(\Rightarrow\dfrac{f\left(x\right)-x.f'\left(x\right)}{f^2\left(x\right)}=1\)

\(\Rightarrow\left(\dfrac{x}{f\left(x\right)}\right)'=1\)

Lấy nguyên hàm 2 vế:

\(\Rightarrow\dfrac{x}{f\left(x\right)}=x+C\)

Thay \(x=1\Rightarrow\dfrac{1}{f\left(x\right)}=1+C\Rightarrow C+1=2\Rightarrow C=1\)

\(\Rightarrow f\left(x\right)=\dfrac{x}{x+1}\Rightarrow P=\dfrac{1}{2}.\dfrac{2}{3}...\dfrac{2021}{2022}=\dfrac{1}{2022}\)

Answer 2

n_Ca(OH)2 = 2.0,01 = 0,02 (mol)