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Examine if Rolle’s theorem is applicable...

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example?`f(x) = [x]` for `x in [-2,2]`

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Verify Rolle’s theorem for the function f(x) = x^2 + 2x - 8, x in [-4,...

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  2. Examine if Rolle’s theorem is applicable to any of the following funct...

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  3. Examine if Rolle’s theorem is applicable to any of the following funct...

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  4. Examine if Rolle’s theorem is applicable to any of the following funct...

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

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  6. Verify Mean Value Theorem, if f(x) = x^2-4x-3, in the interval [a, b],...

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  7. Verify Mean Value Theorem, if f(x) = x^3-5x^2-3x, in the interval [a,...

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  8. Examine the applicability of Mean Value Theorem for all three function...

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

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  10. Differentiate w.r.t. x the function : sin^3x + cos^6 x

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  11. Differentiate w.r.t. x the function : (5x)^(3cos2x)

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  12. Differentiate w.r.t. x the function : sin^-1(xsqrtx), 0lexle1

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  13. Differentiate w.r.t. x the function : (logx)^logx, x>1

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  14. Differentiate w.r.t. x the function : cos(acosx+bsinx), for some const...

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  15. Differentiate w.r.t. x the function : x^x + x^a + a^x + a^a, for some ...

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  16. Differentiate w.r.t. x the function : x^(x^2-3) + (x-3)^(x^2), for x>...

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  17. Find dy/dx if y =12(1-cost), x =10(t-sint)

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  18. Find dy/dx if y = sin^-1x + sin^-1 sqrt(1-x^2), 0ltxlt1

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  19. If xsqrt(1+y) + ysqrt(1+x) = 0 for x lies between -1 and 1 prove that ...

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  20. If cosy = xcos(a+y), with cos a ne +-1, prove that dy/dx = (cos^2(a+y...

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