Giúp mk với Gdhdjdjjxhchcfhcgggg

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Giúp mk với
Gdhdjdjjxhchcfhcgggg
giup-mk-voi-gdhdjdjjhchcfhcgggg

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Lệ Thu 5 years 2021-05-16T21:23:48+00:00 1 Answers 26 views 0

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  1. ngochoa
    0
    2021-05-16T21:25:44+00:00
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    Đáp án:

    $I = 1$

    Giải thích các bước giải:

     Ta có:

    $\begin{array}{l}
    \mathop {\lim }\limits_{x \to 1} \dfrac{{f\left( x \right) – 10}}{{x – 1}} = 5\\
     \Rightarrow \mathop {\lim }\limits_{x \to 1} \left( {f\left( x \right) – 10} \right) = 0\\
     \Rightarrow f\left( 1 \right) – 10 = 0\\
     \Rightarrow f\left( 1 \right) = 10
    \end{array}$

    Lại có;

    $\begin{array}{l}
    \mathop {\lim }\limits_{x \to 1} \dfrac{{f\left( x \right) – 10}}{{x – 1}} = 5\\
     \Rightarrow \mathop {\lim }\limits_{x \to 1} \dfrac{{f\left( x \right) – 10}}{{\sqrt x  – 1}}.\mathop {\lim }\limits_{x \to 1} \dfrac{1}{\sqrt x  + 1}  = 5\\
     \Rightarrow \dfrac{1}{2}\mathop {\lim }\limits_{x \to 1} \dfrac{{f\left( x \right) – 10}}{{\sqrt x  – 1}} = 5\\
     \Rightarrow \mathop {\lim }\limits_{x \to 1} \dfrac{{f\left( x \right) – 10}}{{\sqrt x  – 1}} = 10
    \end{array}$

    Khi đó:

    $\begin{array}{l}
    I = \mathop {\lim }\limits_{x \to 1} \dfrac{{f\left( x \right) – 10}}{{\left( {\sqrt x  – 1} \right)\left( {\sqrt {4f\left( x \right) + 9}  + 3} \right)}}\\
     = \mathop {\lim }\limits_{x \to 1} \dfrac{{f\left( x \right) – 10}}{{\sqrt x  – 1}}.\mathop {\lim }\limits_{x \to 1} \dfrac{1}{{\sqrt {4f\left( x \right) + 9}  + 3}}\\
     = 10.\dfrac{1}{{\sqrt {4.10 + 9}  + 3}}\\
     = 1
    \end{array}$

    Vậy $I = 1$

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