help@askiitians.com

+91-93193 64476

Differential Calculus> find d 2 y/dx 2 (independent of t) of the...

question mark

find d²y/dx² (independent of t) of the function defined paramaterically as x = sin (ln t) and y = cos (ln t)

Satyadip Mahapatra , 10 Years ago

Grade 12

1 Answers

BALAJI ANDALAMALA

x = sin(lnt) and y=cos(lnt)

$x^2+y^2 = sin^2(lnt)+cos^2(lnt) = 1$
The equation satisfies the above two parametric equations is x^2+y^2=1.

Differentiating with respect to x , we get
$2x+2y\frac{dy}{dx}=0.$
$\Rightarrow \frac{dy}{dx}=\frac{-x}{y}............(1)$
Again differentiating equation (1) with respect to x, we get

$\frac{d^2y}{dx^2}=\frac{-1-(\frac{dy}{dx})^2}{y} = \frac{-1-(\frac{-x}{y})^2}{y}$
$\therefore \frac{d^2y}{dx^2}= = \frac{-(y^2+x^2)}{y^3} = \frac{-1}{y^3}$ $(\because \,\,x^2+y^2=1)$

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