Lim x -2a x-a x- x- x-A- log aB- log 2C- aD- log x

The correct option is A log alim_x →π/2 (a^cot x a^cos x/cot x cot x= )= lim_x →π/2 a^cos x ( a^cot x cos x 1/cot x cos x ) =a^cos ( π/2 ) lim_x →π/2 ( a^cot ...

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Byju's Answer

Standard XII

Mathematics

Chain Rule of Differentiation

lim x →π/2a x...

Question

${lim}_{x \to \frac{π}{2}} \frac{a^{c o t x} - a^{c o s x}}{c o t x - c o t x} =$

log a

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log 2

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log x

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Solution

The correct option is A log a
${lim}_{x \to \frac{π}{2}} (\frac{a^{c o t x} - a^{c o s x}}{c o t x - c o t x} =) = {lim}_{x \to \frac{π}{2}} a^{c o s x} (\frac{a^{c o t x - c o s x} - 1}{c o t x - c o s x})$
$= a^{c o s (\frac{π}{2})} {lim}_{x \to \frac{π}{2}} (\frac{a^{c o t x - c o s x} - 1}{c o t x - c o s x}) = 1. l o g a = l o g a$

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Similar questions

lim x \to \frac{π}{2} \frac{a^{cot x} - a^{cos x}}{cot x - cos x} =

Q. The value of

\lim_{x \to 0} \frac{\sqrt{a^{2} - a x + x^{2}} - \sqrt{a^{2} + a x + x^{2}}}{\sqrt{a + x} - \sqrt{a - x}}

is

(a) a

(b)

\sqrt{a}

- \sqrt{a}

lim x \to \infty \frac{x - log x}{x + log x} =

lim x \to \frac{π}{2} \frac{a^{cot x} - a^{cos x}}{cot x - cos x}

is equal to :

\lim_{x \to 0} \frac{\log (a + x) - \log a}{x}

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limx→π2acot x−acos xcot x−cot x=

The correct option is A log alimx→π2(acot x−acos xcot x−cot x=)=limx→π2acos x(acot x−cos x−1cot x−cos x) =acos(π2) limx→π2(acot x−cos x−1cot x−cos x)=1.log a=log a

${lim}_{x \to \frac{π}{2}} \frac{a^{c o t x} - a^{c o s x}}{c o t x - c o t x} =$