Lim x -41- 3 x-2- x-cos 3 x-

The correct option is B 3/4lim_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^ ...

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Byju's Answer

Standard XII

Mathematics

Limit

lim x →π/41- ...

Question

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

\frac{3}{4}

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\frac{1}{2}

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\infty

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Solution

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

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Similar questions

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

is:

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

${lim}_{x \to \frac{π}{4}} \frac{1 - t a n x}{x - \frac{π}{4}}$

Q. Evaluate

lim x \to \frac{π}{4} \frac{1 - tan x}{x - \frac{π}{4}}

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

is:

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limx→π41−cot3x2−cot x−cot3 x=___

The correct option is A 34limx→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

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