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If x=f(t )cost-f^(prime)(t)sint and y=f...

If `x=f(t )cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost ,t h e n((dx)/(dt))^2+((dy)/(dt))^2`

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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

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If x=a(cost+tsint) and y=a(sint-tcost), then find the value of (d^2y)/(dx^2) at t=pi/4

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RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If y=x^(n-1)lnx then x^2y2+(3-2n)x y1 is equal to (a) -(n-1)^2y (b) (...

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  2. If x y-(log)e y=1 satisfies the equation x(y y2+y1 2)-y2+lambday y1=0,...

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  3. If x=f(t )cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost ,t h ...

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  4. If d/(dx){x^n-a1x^(n-1)+a2x^(n-2)++(-1)^n an}e^x=x^n e^x , then the va...

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  5. If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to

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  6. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) ...

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  7. If y=tan^-1((log(e/x^2))/(log(ex^2)))+tan^-1((3+2logx)/(1-6logx)), the...

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  8. If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xy(x)= 1 (b...

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  9. If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)......(cosn x+isinn x)...

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  10. (d^(20))/(dx^(20))(2cosxcos3x)is equal to (a)2^(20)(cos2x-2^(20)cos3x...

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  11. If x=acosn t-bsinn t ,t h e n(d^2x)/(dt^2) is n^2x (b) -n^2x (c) -n ...

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  12. Find order & degree of equation xy ((d^2y)/dx^2)+x(dy/dx)^2-y(dy/dx)=0...

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  13. In (dy)/(dx),x is a independent variable and y is the dependent variab...

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  14. If y^2=a^2cos^2x+b^2sin^2x ,t h e np rov et h a t(d^2y)/(dx^2)+y=(a^2b...

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  15. If y=sin^(-1)x , show that (d^2y)/(dx^2)=x/((1-x^2)^(3//2))

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  16. If y=Acosn x+Bsinn x , show that (d^2y)/(dx^2)+n^2\ y=0 .

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  17. If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n ...

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  18. If y=Acos(logx)+\ Bsin(logx) , prove that x^2\ (d^2y)/(dx^2)+x(dy)/(dx...

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  19. If y=tanx+secx , prove that (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

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  20. If y=tanx , prove that y2=2y y1 .

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