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If y=5cosx-3sinx, prove that (d^2y)/(dx^...

If `y=5cosx-3sinx,` prove that `(d^2y)/(dx^2)+y=0`

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A N EXCEL PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Find the second order derivative of the following functions log(logx)

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  2. Find the second order derivative of the following functions sin(logx)

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  3. If y=5cosx-3sinx, prove that (d^2y)/(dx^2)+y=0

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  4. If y=cos^-1x, find (d^2y)/(dx^2) in terms of y alone.

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  5. Let y=3cos(logx)+4sin(logx) Prove that x^2y2+xy1+y=0

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  6. If y=ae^(mx)+be^(nx) , show that (d^2y)/(dx^2)-(m+n)dy/dx+mny=0

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  7. If y=500e^(7x)+600e^(-7x). Show that (d^2y)/(dx^2)=49y

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

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  9. If y=(tan^(-1)x)^2, show that (x^2+1)^2y2+2x(x^2+1)y1=2 .

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  10. Verify Rolle's Theorem for the function f(x)=x^2+2x-8 , x in [-4,2]

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  11. Examine if Rolle's theorem is applicable to any of the following funct...

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  12. Examine if Rolle's theorem is applicable to any of the following funct...

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  13. Examine if Rolle's theorem is applicable to any of the following funct...

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  14. If f:[-5,5]toR is a differentiable function and if f'(x) does not vani...

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  15. Verify mean value theorem for the function f(x)=x^2-4x-3 in the interv...

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  16. Verify Lagrange 's mean value theorem, if f(x)=x^3-5x^2-3x in the inte...

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  17. Differentiate the following w.r.t x (3x^2-9x+5)^9

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  18. Differentiate the following w.r.t x sin^3x+cos^6x

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  19. Differentiate the following w.r.t x (5x)^(3cos2x)

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  20. Differentiate the following w.r.t x (logx)^(logx),xgt1

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