If x=f(t )cost-f^(prime)(t)sinta n dy=f...

If x=`f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h e n((dx)/(dt))^2+((dy)/(dt))^2` (a) `f(t)-f^(primeprime)(t)` (b) `{f(t)-f^(primeprime)(t)}^2` (c) `{f(t)+f^(primeprime)(t)}^2` (d) none of these

Text Solution

Verified by Experts

Given,`x= f(t) cost - f'(t) sint`
` y = f(t) sint + f'(t) cost `
`(dx)/(dt)=f′(t)cost−f(t)sint−f′′(t)sint−f′(t)cost`
= `-f(t) sint - f''(t) sint `
=` -sint[f(t) + f''(t)] `
`dy/dt=f′(t)sint−f(t)cost−f′′(t)sint−f′(t)sint `
=` -f(t) cost - f''(t) cost `
= `cost[f(t) + f''(t)]`
...

Topper's Solved these Questions

FUNCTION
RD SHARMA|Exercise Solved Examples And Exercises|393 Videos
INCREASING AND DECREASING FUNCTION
RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

Similar Questions

Explore conceptually related problems

If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ((dx)/(dt))^2+((dy)/(dt))^2= (a) f(t)-f^(primeprime)(t) (b) {f(t)-f^(primeprime)(t)}^2 (c) {f(t)+f^(primeprime)(t)}^2 (d) none of these

If =f''(t)cos t+f'(t)sin t,y=-f''(t)sin t+f'(t)cos t, then int[((dx)/(dt))^(2)+((dy)/(dt))^(2)]^((1)/(2))dt is equal to

Let f(t)="ln"(t) . Then, (d)/(dx)(int_(x^(2))^(x^(3))f(t)" dt")

if x=(1+t)/(t^(3)),y=(3)/(2t^(2))+(2)/(t) satisfies f(x)*{(dy)/(dx)}^(3)=1+(dy)/(dx) then f(x) is:

Off(x)=int_0^x("cos"(sint)+"cos"(cost)dt ,t h e nf(x+pi)i s (a)f(x)+f(pi) (b) f(x)+2(pi) (c)f(x)+f(pi/2) (d) f(x)+2f(pi/2)

If F(x)=int_(1)^(x)(ln t)/(1+t+t^(2))dt then F(x)=-F((1)/(x))

f(x)=int_(0)^( pi)f(t)dt=x+int_(x)^(1)tf(t)dt, then the value of f(1) is (1)/(2)

If f(-x)+f(x)=0 then int_(a)^(x)f(t)dt is

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises

If y=x^(n-1)lnx then x^2y2+(3-2n)x y1 is equal to -(n-1)^2y (b) (n...
Text Solution
|
If x y-(log)e y=1 satisfies the equation x(y y2+y1 2)-y2+lambday y1=0,...
Text Solution
|
If x=f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h ...
Text Solution
|
If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to
Text Solution
|
Let f(x) be a polynomial.Then, the second order derivative of f(e^x) ...
Text Solution
|
If y=tan^-1((log(e/x^2))/(log(ex^2)))+tan^-1((3+2logx)/(1-6logx)), the...
Text Solution
|
If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)fx-xy(x)= 1 (b) -1...
Text Solution
|
If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)......(cosn x+isinn x)...
Text Solution
|
(d^(20))/(dx^(20))(2cosxcos3x)is equal to (a)2^(20)(cos2x-2^(20)cos3x...
Text Solution
|
If x=acosn t-bsinn t ,t h e n(d^2x)/(dt^2) is n^2x (b) -n^2x (c) -n ...
Text Solution
|
In (dy)/(dx),x is a independent variable and y is the dependent vari...
Text Solution
|
If y^2=a^2cos^2x+b^2sin^2x then prove that (d^2y)/(dx^2)+y=(a^2b^2)/(y...
Text Solution
|
If y=sin^(-1)x , show that (d^2y)/(dx^2)=x/((1-x^2)^(3//2))
Text Solution
|
If y=Acosn x+Bsinn x , show that (d^2y)/(dx^2)+n^2\ y=0 .
Text Solution
|
If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n ...
Text Solution
|
If y=Acos(logx)+\ Bsin(logx) , prove that x^2\ (d^2y)/(dx^2)+x(dy)/(dx...
Text Solution
|
If y=tanx+secx , prove that (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)
Text Solution
|
If y=tanx , prove that y2=2y y1 .
Text Solution
|
If y=tan^(-1)x , find (d^2y)/(dx^2) in terms of y alone.
Text Solution
|
If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0 .
Text Solution
|