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If y=A e^(-k t)cos(p t+c), then prove th...

If `y=A e^(-k t)cos(p t+c),` then prove that `(d^2y)/(dt^2)+2k(dy)/(dx)+n^2y=0` , where `n^2=p^2+k^2`

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RESONANCE DPP ENGLISH-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Find (dy)/(dx), when xa n dy are connected by the following relations ...

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  2. Let : f(x)={(sina x^2)/(x^2),x!=0 3/4+1/(4a),x=0 for what values of a...

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  3. If y=A e^(-k t)cos(p t+c), then prove that (d^2y)/(dt^2)+2k(dy)/(dx)+n...

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  4. (d^2x)/(dy^2) equals: ((d^2y)/(dx^2))^(-1) (b) -((d^2y)/(dx^2))^(-1)(...

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  5. If x=a t^2,y=2a t , then (d^2y)/(dx^2) is equal to (a)-1/(t^2) (b...

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  6. If x=(1+t)/(t^3),y=3/(2t^2)+2/t , then x((dy)/(dx))^3-(dy)/(dx) is e...

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  7. If e^y(x+1)=1, show that (d^(2y))/(dx^2)=((dy)/(dx))^2 If y=sin(2sin^...

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  8. Evaluate : ("lim")(xvec2a^+)(sqrt(x-2a)+sqrt(x)-sqrt(2a))/sqrt(x^2-4a^...

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  9. Evaluate: lim(x to 0^+)((e^(xln(2^(x-1)))-(2^x-1)^xsinx)/(e^(x lnx)))...

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  10. Let f(x)=[(sinx)/x]+[(2sin2x)/x]++[(10sin10 x)/x] (where [.] is the gr...

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  11. The sum of the series x/(1!)+(2x^2)/(2!)+(3x^3)/(3!)+ is x e^x b. -x e...

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  12. If a x^2+2h x y+b y^2=0, then (dy)/(dx) is equal to y/x (b) x/y (c) ...

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  13. If f(x)=(log)x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e ...

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  14. Let y=x^(3)-8x+7 and x=f(t)." If "(dy)/(dt)=2 and x=3 at t = 0," then ...

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  15. If x=(1+t)/(t^(3)),y=(3)/(2t^(2))+(2)/(t) satisfy f(x)((dy)/(dx))^(3)=...

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  16. Let f(x) ={{:((x-4)/(|x-4|)+a,xlt4),(a+b,x=4),( (x-4)/(|x-4|)+b, x gt4...

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  17. The point(s) of minimum of function, f(x)=4x^3-x|x-2|,x in [0,3] is x=...

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  18. Let g(x)=log(e)f(x) where f(x) is twice differentiable positive functi...

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  19. Let f:""(1,""1)vecR be a differentiable function with f(0)""=""-1""a...

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  20. If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(d...

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