help@askiitians.com

+91-93193 64476

Differential Calculus> Evaluate the following...

question mark

Evaluate the following

Aninda Chakrabarty , 10 Years ago

Grade 12th pass

1 Answers

jagdish singh singh

$\hspace{-0.5 cm} $Let $\bf{\mathcal{A} = \lim_{x\rightarrow \infty}\frac{\sin x+\cos x}{x^2}\;,}$ Now Using $\bf{\sin x+\cos x = \sqrt{2}\sin \left(x+\frac{\pi}{4}\right)}$\\\\ \\And Using $\bf{-\sqrt{2} \leq \sqrt{2}\sin \left(x+\frac{\pi}{4}\right) \leq \sqrt{2}}$\\\\\\ So we get $\bf{-\lim_{x\rightarrow \infty}\frac{\sqrt{2}}{x^2}\leq \lim_{x\rightarrow \infty}\frac{\sqrt{2}\sin (x+\frac{\pi}{4})}{x^2}\leq \lim_{x\rightarrow \infty}\frac{\sqrt{2}}{x^2}}$\\\\\\$

$\hspace{-0.5 cm} $So we get $\bf{-0\leq \mathcal{A}\leq 0}$\\\\\\ So Using Squeeze Theorem, We get $\bf{\mathcal{A} =0}$$

Last Activity: 10 Years ago

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to move once over to level a playground. find the area of the playground in square m?

differential calculus

1 Answer Available

Last Activity: 3 Years ago

Find dy/DX when y=x^sinx+sin-1√x.

Please give me the solution of this problem.

differential calculus

1 Answer Available

Last Activity: 3 Years ago

If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.

differential calculus

1 Answer Available

Last Activity: 3 Years ago

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

View all Questions