Tìm các giới hạn các hàm số sau
a) lim (x-> âm vô cùng) (x+3)( căn (x^2+3x+2) )
b) lim(x->1) (4x^3-6x^2+3x-1) / (-x^2+4x-3)
Tìm các giới hạn các hàm số sau a) lim (x-> âm vô cùng) (x+3)( căn (x^2+3x+2) ) b) lim(x->1) (4x^3-6x^2+3x-1) / (-x^2+4x-3)
By Vivian
a,
$\lim\limits_{x \to – \infty} \dfrac{x+3}{\sqrt{x^2+3x+2}}$
$\lim\limits_{x \to – \infty} \dfrac{1}{-1} =-1$
b,
$\lim\limits_{x \to 1} \dfrac{4x^3-6x^2+3x-1}{-x^2+4x – 3}$
$\lim\limits_{x \to 1} \dfrac{(x-1)(4x^2-2x+1)}{(x-1)(x-3)}$
$\lim\limits_{x \to 1} \dfrac{4x^2-2x+1}{x-3}$
$\lim\limits_{x \to 1} \dfrac{-3}{2}$
$= \dfrac{-3}{2}$
`a)`
`lim_{x->-oo} (x+3)(\sqrt{x^2+3x+2})`
`= lim_{x->-oo}(x+3) . lim_{x->-oo} (\sqrt{x^2+3x+2})`
`= (-oo) . oo`
`= -oo`
`b)`
`lim_{x->1} (4x^3-6x^2+3x-1)/(-x^2+4x-3)`
`= lim_{x->1} (-(4x^2 – 2x + 1)/(x-3) )`
`= -(4.1^2 – 2.1 + 1)/(1-3)`
`= 3/2`