Question

[Trúc Phạm]

Giúp e giải chi tiết câu 17 bà 21 đi ạ

Answer 1

[Nguyễn Lê Phước Thịnh]

21:

\(y'=\dfrac{\left(x^2-3x+5\right)'\left(x+2\right)-\left(x+2\right)'\left(x^2-3x+5\right)}{\left(x+2\right)^2}\)

\(=\dfrac{\left(2x-3\right)\left(x+2\right)-\left(x^2-3x+5\right)}{\left(x+2\right)^2}\)

\(=\dfrac{2x^2+4x-3x-6-x^2+3x-5}{\left(x+2\right)^2}=\dfrac{x^2+4x-11}{\left(x+2\right)^2}\)

17:

Khi x<>0 thì \(\lim\limits_{x\rightarrow0}f\left(x\right)=\lim\limits_{x\rightarrow0}\dfrac{1+4x-1}{\sqrt{1+4x}+1}\cdot\dfrac{1}{x}\)

\(=\lim\limits_{x\rightarrow0}\dfrac{4}{\sqrt{1+4x}+1}=\dfrac{4}{1+1}=\dfrac{4}{2}=2\)

=>Chọn B