lim x->1 (x^2-1)/(((căn x^2) +3) + ((căn x) -3))

Question

lim x->1 (x^2-1)/(((căn x^2) +3) + ((căn x) -3))

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Kinsley 2 tuần 2021-11-25T00:10:16+00:00 1 Answers 1 views 0

Answers ( )

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    2021-11-25T00:11:41+00:00

    Đáp án: 2

     

    Giải thích các bước giải:

    $\begin{array}{l}
    \mathop {\lim }\limits_{x \to 1} \frac{{{x^2} – 1}}{{\sqrt {{x^2} + 3}  + \sqrt x  – 3}}\\
     = \mathop {\lim }\limits_{x \to 1} \frac{{\left( {x – 1} \right)\left( {x + 1} \right)}}{{\sqrt {{x^2} + 3}  – 2 + \sqrt x  – 1}}\\
     = \mathop {\lim }\limits_{x \to 1} \frac{{\left( {x – 1} \right)\left( {x + 1} \right)}}{{\frac{{{x^2} – 1}}{{\sqrt {{x^2} + 3}  + 2}} + \frac{{x – 1}}{{\sqrt x  + 1}}}}\\
     = \mathop {\lim }\limits_{x \to 1} \frac{{x + 1}}{{\frac{{x + 1}}{{\sqrt {{x^2} + 3}  + 2}} + \frac{1}{{\sqrt x  + 1}}}}\\
     = \frac{{1 + 1}}{{\frac{{1 + 1}}{{\sqrt {1 + 3}  + 2}} + \frac{1}{{1 + 1}}}} = 2
    \end{array}$

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