Lim x -6 2 x-3-cosec x-2

Lim_x→π/6cot^2x 3/cosecx 2 =lim_x→π/6cosec^2x 1 3/cosecx 2 =lim_x→π/6cosec^2x 4/cosecx 2 =lim_x→π/6(cosecx 2)(cosecx+2)/(cosecx 2) =lim_x→π/6(cosecx+2) =cosecπ/ ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x →π/6 2 ...

Question

${lim}_{x \to \frac{π}{6}} \frac{c o t^{2} x - 3}{c o s e c x - 2}$

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Solution

${lim}_{x \to \frac{π}{6}} \frac{c o t^{2} x - 3}{c o s e c x - 2}$

$= {lim}_{x \to \frac{π}{6}} \frac{c o s e c^{2} x - 1 - 3}{c o s e c x - 2}$

$= {lim}_{x \to \frac{π}{6}} \frac{c o s e c^{2} x - 4}{c o s e c x - 2}$

$= {lim}_{x \to \frac{π}{6}} \frac{(c o s e c x - 2) (c o s e c x + 2)}{(c o s e c x - 2)}$

$= {lim}_{x \to \frac{π}{6}} (c o s e c x + 2)$

$= c o s e c \frac{π}{6} + 2$

=2+2=4

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Similar questions

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lim x \to \frac{π}{6} \frac{{cot}^{2} x - 3}{cos e c x - 2}

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Q. The value of

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limx→π6cot2x−3cosecx−2

limx→π6cot2x−3cosecx−2 =limx→π6cosec2x−1−3cosecx−2 =limx→π6cosec2x−4cosecx−2 =limx→π6(cosecx−2)(cosecx+2)(cosecx−2) =limx→π6(cosecx+2) =cosecπ6+2 =2+2=4

${lim}_{x \to \frac{π}{6}} \frac{c o t^{2} x - 3}{c o s e c x - 2}$