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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-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 and 3/4+1/(4a); x=0dot For what v...

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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: (1) ((d^2y)/(dx^2))^-1 (2) -((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))/(x^2-4a^2)

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  9. Evaluate: ("lim")(xvec2a^+)((e^x I n(2^(x-1))-(2^x-1)^xsinx)/(e^(x I n...

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  10. If f^(prime)(k)=l ,t h e nl= 0 (b) 4/5 (c) pi/2 (d) (16)/5

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  11. f^(prime)(l+3)= 0 (b) 2/5 (c) -2/5 (d) -4/5

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  12. Comprehension (for Q. No. 1 to 3) Let f(x)=sin^(-1)(1-x^2)/(1+x^2)+tan...

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  13. Solve for x , if [cos^(-1)x]=[sin^(-1)x] (where [.] represents greates...

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  14. underset(x to0)(lim)((1+a^(3))+8e^(1//x))/(1+(1-b^(3))e^(1//x))=2 " th...

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  15. Which of the following is true? pi/3>tan^(-1)pi/3 (b) pi/3<tan^(-1)pi...

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

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

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  18. 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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  19. 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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  20. Let y=x^3-8x+7a n dx=f(t)dot If (dy)/(dt)=2 and x=3 at t=0, then (dx)/...

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