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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 [5,9]`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Examine if Rolle’s theorem is applicable to any of the following funct...

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  2. If f(x)= {(kx^2,,x,<,2),(3,,x,ge,2):} is continuous at x = 2, then the...

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  3. Check the continuity of the function f given by f(x) = 2x+3 at x=1

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  4. Check the continuity of the following functions: f(x) = x^2atx=0

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

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  6. Examine the function f(x) = 2x^2-5 for its continuity at the point x =...

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  7. Is the function defined by f(x) = |x|, a continuous function?

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  8. Find the point at which the function f(x) = [x] is not continuous in (...

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  9. Examine the following function for continuity: f(x) = x-5

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  10. Examine the following functions for continuity: f(x) = x^3 + x^2-1

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  11. Examine the following function for continuity: f(x) = 1/(x-5), x ne 5

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  12. Examine the following function for continuity: f(x) = (x^2 -25)/(x+5),...

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  13. Examine the following function for continuity: f(x) = |x-5|

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  14. Prove that the following functions are continuous at all points of the...

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  15. Prove that the following functions are continuous at all points of the...

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  16. Prove that the following functions are continuous at all points of the...

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  17. Discuss the continuity of the following function: f(x) = sinx + cosx

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  18. Discuss the continuity of the following function: f(x) = sinx cdot cos...

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  19. Discuss the continuity of the following function: f(x) = sinx cdot cos...

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  20. Discuss the continuity of the following functions: f(x) = (sinx)/(co...

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  21. Prove that f(x) = |sin x| is continous at all point of its domnin.

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