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Verify the Rolle's theorem for each of t...

Verify the Rolle's theorem for each of the function in following questions:
`f(x)= x(x-1)^(2), " in" x in [0, 1]`

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The correct Answer is:
`(1)/(3) in (0, 1)`
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-NCERT Exemplar Problems and Solution (Short Answer Type Questions)
  1. If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y), then prove that (dy)/(dx)= ...

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

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  3. Verify the Rolle's theorem for each of the function in following quest...

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  4. Verify the Rolle's theorem for each of the function in following quest...

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  6. Verify the Rolle's theorem for each of the function in following quest...

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  7. Verify the Rolle's theorem for each of the function in following quest...

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  8. Discuss the applicability of Rolle's theorem on the function given by ...

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  9. Find the points on the curve y= cos x-1 in x in [0, 2pi], where the ta...

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  10. Using Rolle's theorem, find the point on the curve y= x (x-4), x in [0...

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  11. Verify mean value theorem for each of the functions: f(x) = (1)/(4x-...

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  12. Verify mean value theorem for each of the functions: f(x)= x^(3)-2x...

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  13. Verify mean value theorem for each of the functions: f(x)= sin x- s...

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  14. Verify mean value theorem for each of the functions: f(x)= sqrt(25-...

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  15. Find a point on the curve y= (x-3)^(2), where the tangent is parallel ...

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  16. Using mean value theorem, prove that there is a point on the curve y= ...

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  17. Examine the continuity of the function f(x)= x^(3) + 2x^(2)-1 " at "...

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  18. Examine the continuity of the function f(x) = {(3x+5",","if " x ge 2...

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  19. Examine the continuity of the function f(x)= {((1-cos(2x))/(x^(2)),...

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  20. Examine the continuity of the function f(x)= {((2x^(2)-3x-2)/(x-2)",...

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