Giúp mk với Fxuycx7rxx7x7x7tx0ux7r7x7t7tt8 Question Giúp mk với Fxuycx7rxx7x7x7tx0ux7r7x7t7tt8 in progress 0 Môn Toán Thiên Thanh 5 years 2021-05-17T02:57:52+00:00 2021-05-17T02:57:52+00:00 2 Answers 25 views 0
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Đáp án:
$I=2$
Giải thích các bước giải:
Ta có:
$\begin{array}{l}
\mathop {\lim }\limits_{x \to 1} \dfrac{{f\left( x \right) – 16}}{{x – 1}} = 24\\
\Rightarrow \mathop {\lim }\limits_{x \to 1} \left( {f\left( x \right) – 16} \right) = 0\\
\Rightarrow f\left( 1 \right) – 16 = 0\\
\Rightarrow f\left( 1 \right) = 16
\end{array}$
Lại có:
$\begin{array}{l}
I = \mathop {\lim }\limits_{x \to 1} \dfrac{{f\left( x \right) – 16}}{{\left( {x – 1} \right)\left( {\sqrt {2f\left( x \right) + 4} + 6} \right)}}\\
= \mathop {\lim }\limits_{x \to 1} \dfrac{{f\left( x \right) – 16}}{{x – 1}}.\mathop {\lim }\limits_{x \to 1} \dfrac{1}{{\sqrt {2f\left( x \right) + 4} + 6}}\\
= 24.\dfrac{1}{{\sqrt {2.16 + 4} + 6}}\\
= 2
\end{array}$
Vậy $I=2$