Limx- -41-3x-2- x-3x is-

The correct option is C 34 lim_x→π /41 ^3x/2 x ^3x #160; =lim_x→π /41 ^3x/1 x+1 ^3x lim_x→π/4(1 x)(1+ x+ ^2x)1 x+(1 x)(1+ x+ ^2x) ...

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Byju's Answer

Standard XII

Mathematics

Substitution Method to Remove Indeterminate Form

limx→π /41-3x...

Question

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

\frac{11}{4}

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\frac{3}{4}

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\frac{1}{2}

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- \frac{1}{2}

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Solution

The correct option is C $\frac{3}{4}$
$lim x \to π / 4 \frac{1 - {cot}^{3} x}{2 - cot x - {cot}^{3} x}$

$= lim x \to π / 4 \frac{1 - {cot}^{3} x}{1 - cot x + 1 - {cot}^{3} x}$

$lim x \to π / 4 \frac{(1 - cot x) (1 + cot x + {cot}^{2} x)}{1 - cot x + (1 - cot x) (1 + cot x + {cot}^{2} x)}$ ....... Using $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$

$= lim x \to π / 4 \frac{1 + cot x + {cot}^{2} x}{2 + cot x + {cot}^{2} x} = \frac{1 + 1 + 1}{2 + 1 + 1} = \frac{3}{4}$

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Similar questions

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 \infty {[\frac{3 x - 4}{3 x + 2}]}^{\frac{x + 1}{3}}

Evaluate the following one sided limits:

$(i) {lim}_{x \to 2^{+}} \frac{x - 3}{x^{2} - 4}$

$(i i) {lim}_{x \to 2^{-}} \frac{x - 3}{x^{2} - 4}$

$(i i i) {lim}_{x \to 0^{+}} \frac{1}{3 x}$

$(i v) {lim}_{x \to 8^{+}} \frac{2 x}{x + 8}$

$(v) {lim}_{x \to 0^{+}} \frac{2}{x^{\frac{1}{5}}}$

$(v i) {lim}_{x \to \frac{π^{-}}{2}} t a n x$

$(v i i) {lim}_{x \to \frac{π}{2^{+}}} s e c x$

$(v i i i) {lim}_{x \to 0^{-}} \frac{x^{2} - 3 x + 2}{x^{3} - 2 x^{2}}$

$(i x) {lim}_{x \to - 2^{+}} \frac{x^{2} - 1}{2 x + 4}$

$(x) {lim}_{x \to 0^{+}} (2 - c o t x)$

$(x i) {lim}_{x \to 0^{-}} 1 + c o s e c x$

Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

\int \frac{1}{[(x - 1)^{3} (x + 2)^{5}]^{1 / 4}} d x

is equal to

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limx→π/41−cot3x2−cotx−cot3x is:

The correct option is C 34limx→π/41−cot3x2−cotx−cot3x =limx→π/41−cot3x1−cotx+1−cot3xlimx→π/4(1−cotx)(1+cotx+cot2x)1−cotx+(1−cotx)(1+cotx+cot2x) ....... Using a3−b3=(a−b)(a2+ab+b2)=limx→π/41+cotx+cot2x2+cotx+cot2x=1+1+12+1+1=34

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