Question

Answer 1

\(\left(x^2-1\right).f'\left(x\right)=4x-2x.f\left(x\right)\)

\(\Leftrightarrow\left(x^2-1\right).f'\left(x\right)+2x.f\left(x\right)=4x\)

\(\Leftrightarrow\left[\left(x^2-1\right).f\left(x\right)\right]'=4x\)

Lấy nguyên hàm 2 vế:

\(\Rightarrow\left(x^2-1\right).f\left(x\right)=\int4xdx=2x^2+C\)

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

Do \(f'\left(x\right)\) liên tục trên R \(\Rightarrow C=-2\)

\(\Rightarrow f\left(x\right)=2;\forall x\)

\(\Rightarrow f\left(2\right)=2\)