Limx -41 - cot3 x-2 - cot x - cot3 x-

Lim_x →π/41 cot^3 x/2 cot x cot^3 x =lim_x →π/4(1 cot x)(1+ cot x +cot^2 x)/(1 cot x)(cot^2 x+cot x+2) = lim_x →π/4(1+ cot x +cot^2 x)/(cot^2 x+cot x+2) = 1+1 ...

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Byju's Answer

Standard XIII

Mathematics

Limit

limx →π/41 - ...

Question

$l i m_{x \to \frac{π}{4}} \frac{1 - c o t^{3} x}{2 - c o t x - c o t^{3} x} =$ ___

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$\frac{3}{4}$

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$\frac{1}{2}$

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$\infty$

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Solution

The correct option is B
$\frac{3}{4}$

$l i m_{x \to \frac{π}{4}} \frac{1 - c o t^{3} x}{2 - c o t x - c o t^{3} x} = {lim}_{x \to \frac{π}{4}} \frac{(1 - c o t x) (1 + c o t x + c o t^{2} x)}{(1 - c o t x) (c o t^{2} x + c o t x + 2)} = {lim}_{x \to \frac{π}{4}} \frac{(1 + c o t x + c o t^{2} x)}{(c o t^{2} x + c o t x + 2)} = \frac{1 + 1 + 1}{1 + 1 + 2} = \frac{3}{4}$

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Similar questions

lim x \to \frac{π}{4} \frac{1 - c o t^{3} x}{2 - c o t x - c o t^{3} x}

is:

Q. Prove that:

cot x cot 2 x - cot 2 x cot 3 x - cot 3 x cot x = 1

l i m_{x \to \frac{π}{4}} \frac{1 - c o t^{3} x}{2 - c o t x - c o t^{3} x} =

___

Q. The value of

cot 2 x cot x - cot 3 x cot 2 x - cot 3 x cot x

for all permissible values of

x

is,

lim x \to π / 4 \frac{1 - {cot}^{3} x}{2 - cot x - {cot}^{3} x}

is:

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limx→π41−cot3x2−cot x−cot3 x=___

The correct option is B 34 limx→π41−cot3 x2−cot x−cot3 x=limx→π4(1−cot x)(1+cot x+cot2 x)(1−cot x)(cot2 x+cot x+2)=limx→π4(1+cot x+cot2 x)(cot2 x+cot x+2)=1+1+11+1+2=34

$l i m_{x \to \frac{π}{4}} \frac{1 - c o t^{3} x}{2 - c o t x - c o t^{3} x} =$ ___