Limx- 2x5-x-32-2-x3-x-8-2-

The correct option is B 447 Given limit is #160; lim _ x→ 2 x ^ 5 √( x ) 32√( 2 ) #160;/ x ^ 3 √( x ) 8√( 2 ) #160; #160; ⇒ #160;lim ...

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Byju's Answer

Standard XII

Mathematics

Substitution Method to Remove Indeterminate Form

limx→ 2x5√x-3...

Question

$lim x \to 2 \frac{x^{5} \sqrt{x} - 32 \sqrt{2}}{x^{3} \sqrt{x} - 8 \sqrt{2}}$ =

\frac{22}{7}

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\frac{44}{7}

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Solution

The correct option is B $\frac{44}{7}$

Given limit is
$lim x \to 2 \frac{x^{5} \sqrt{x} - 32 \sqrt{2}}{x^{3} \sqrt{x} - 8 \sqrt{2}}$

$\Rightarrow lim x \to 2 \frac{x^{5} \sqrt{x} - 2^{5} \sqrt{2}}{x^{3} \sqrt{x} - 2^{3} \sqrt{2}}$

$\Rightarrow lim x \to 2 \frac{x^{\frac{11}{2}} - 2^{5} \sqrt{2}}{x^{\frac{7}{2}} - 2^{3} \sqrt{2}}$

Applying L' hospital Rule , we get
$\Rightarrow lim x \to 2 \frac{\frac{11}{2} x^{\frac{11}{2} - 1} - 0}{\frac{7}{2} x^{\frac{7}{2} - 1} - 0}$

$\Rightarrow lim x \to 2 \frac{11 x^{4.5}}{7 x^{2.5}}$

$\Rightarrow lim x \to 2 \frac{11 x^{2}}{7} = \frac{11}{7} 2^{2} = \frac{44}{7}$

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Similar questions

lim x \to - 2 \frac{x^{5} + 32}{x^{3} + 8}

{lim}_{x \to 2} \frac{x^{5} - 32}{x^{3} - 8} =

{lim}_{x \to 2} \frac{x^{5} - 32}{x^{3} - 8}

You are given
$cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} . . . . . .$ ;
$sin x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} . . . . . .$ ;
$tan x = x + \frac{x^{3}}{3} + \frac{2 x^{5}}{15} . . . . . .$
Then the value of
$lim x \to 0 \frac{x cos x + sin x}{x^{2} + tan x}$ is

___

Evaluate $l i m x \to 2 (\frac{x^{5} - 32}{x^{3} - 8})$

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limx→2x5√x−32√2x3√x−8√2=

The correct option is B 447Given limit is limx→2x5√x−32√2x3√x−8√2⇒limx→2x5√x−25√2x3√x−23√2 ⇒limx→2x112−25√2x72−23√2Applying L' hospital Rule , we get⇒limx→2112x112−1−072x72−1−0⇒limx→211x4.57x2.5⇒limx→211x27=11722=447

$lim x \to 2 \frac{x^{5} \sqrt{x} - 32 \sqrt{2}}{x^{3} \sqrt{x} - 8 \sqrt{2}}$ =