Lim x - acos-x-cos-a-x-a

Lim_x → acos√(x) cos √(a)/x a =lim_x → a 2 sin(√(x)+√(a)/2)sin(√(x) √(a)/2)/(√(x) √(a))(√(x)+√(a)) = 2 lim_x → asin (√(x)+√(a)/2)×lim_x → a sin(√(x) √(a)/2)/lim ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

lim x → acos√...

Question

${lim}_{x \to a} \frac{c o s \sqrt{x} - c o s \sqrt{a}}{x - a}$

Open in App

Solution

${lim}_{x \to a} \frac{c o s \sqrt{x} - c o s \sqrt{a}}{x - a}$

$= {lim}_{x \to a} \frac{- 2 s i n (\frac{\sqrt{x} + \sqrt{a}}{2}) s i n (\frac{\sqrt{x} - \sqrt{a}}{2})}{(\sqrt{x} - \sqrt{a}) (\sqrt{x} + \sqrt{a})}$

$= - 2 {lim}_{x \to a} \frac{s i n (\frac{\sqrt{x} + \sqrt{a}}{2}) \times {lim}_{x \to a} s i n (\frac{\sqrt{x} - \sqrt{a}}{2})}{{lim}_{x \to a} (\sqrt{x} + \sqrt{a}) \times (\frac{\sqrt{x} - \sqrt{a}}{2})} \times \frac{1}{2}$

$= - 2 s i n \sqrt{a} \times 1 \times \frac{1}{2 \sqrt{a}} \times \frac{1}{2}$

$= - \frac{1}{2 \sqrt{a}} s i n \sqrt{a}$

Suggest Corrections

Similar questions

Q. Evaluate:-

lim x \to a \frac{cos \sqrt{x} - cos \sqrt{a}}{x - a}

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

Find the derivative of e^{a cos-1 x}

Q. Evaluate

lim x \to a \frac{cos \sqrt{x} - cos \sqrt{a}}{x - a}

Q. If

lim x \to 0 (\frac{c o s 4 x + a c o s 2 x + b}{x^{4}})

is finite then the value of

a, b

respectively are?

Join BYJU'S Learning Program

limx→acos√x−cos√ax−a

limx→acos√x−cos√ax−a =limx→a−2 sin(√x+√a2)sin(√x−√a2)(√x−√a)(√x+√a) =−2limx→asin(√x+√a2)×limx→asin(√x−√a2)limx→a(√x+√a)×(√x−√a2)×12 =−2 sin √a×1×12√a×12 =−12√asin√a

${lim}_{x \to a} \frac{c o s \sqrt{x} - c o s \sqrt{a}}{x - a}$