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)

Question

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)

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Vivian 2 tháng 2021-08-07T18:49:49+00:00 2 Answers 4 views 0

Answers ( )

    0
    2021-08-07T18:50:55+00:00

     a, 

    $\lim\limits_{x \to – \infty} \dfrac{x+3}{\sqrt{x^2+3x+2}}$

    $\lim\limits_{x \to –  \infty} \dfrac{1}{-1} =-1$

    b, 

    $\lim\limits_{x \to 1} \dfrac{4x^3-6x^2+3x-1}{-x^2+4x – 3}$

    $\lim\limits_{x \to 1} \dfrac{(x-1)(4x^2-2x+1)}{(x-1)(x-3)}$

    $\lim\limits_{x \to 1} \dfrac{4x^2-2x+1}{x-3}$

    $\lim\limits_{x \to 1} \dfrac{-3}{2}$

    $= \dfrac{-3}{2}$

    0
    2021-08-07T18:51:48+00:00

    `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`

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