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If f:[-5,5]toR is a differentiable funct...

If `f:[-5,5]toR` is a differentiable function and if f'(x) does not vanish any where, then prove that `f(-5)nef(5)`

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A N EXCEL PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let y=3cos(logx)+4sin(logx) Prove that x^2y2+xy1+y=0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Differentiate the following w.r.t.x x^x+x^a+a^x+a^a for some fixed agt...

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  18. Find dy/dx,if y=12(1-cost),x=10(t-sint).pi/2lttltpi/2

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  19. If x= a(cos t +t sin t) and y=a(sin t - t cos t), find (d^2y)/(dx^2)

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  20. If y=e^(acos^-1x) , then show that (1-x^2)y2-xy1-a^2y=0

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