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Verify the Rolle's theorem for the follo...

Verify the Rolle's theorem for the following functions:
(a) `f(x) = x^(4)-1` on the interval `[-1,1]`
(b) `f(x) = e^(x) (sin x- cos x)` in `(pi/4, (5pi)/4)`

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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (4)
  1. Discuss the applicability of Rolle's theorem of the following function...

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  2. Discuss the applicability the Rolle's theorem for the function f(x) = ...

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  3. Discuss the applicability of Rolle's theorem of the following function...

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  4. Discuss the applicability of Rolle's theorem of the following function...

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  5. Discuss the applicability of Rolle's theorem of the following function...

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  6. Discuss the applicability of Rolle's theorem of the following function...

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  7. Discuss the applicability of Rolle's theorem of the following function...

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  8. Discuss the applicability of Rolle's theorem of the following function...

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  9. Discuss the applicability of Rolle's theorem of the following function...

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  10. Show that between any two roots of e^(x) cos x=1, there exists at leas...

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  11. Let a(0)/(n+1) +a(1)/n + a(2)/(n-1) + ….. +(a(n)-1)/2 +a(n)=0. Show th...

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  12. Verify the Rolle's theorem for the following functions: (a) f(x) = x^...

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  13. f(x) = |{:(sin x, sin alpha, sin beta),(cos x, cos alpha, cos beta),(t...

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  14. A function f(x) is, continuous in the closed interval [0,1] and differ...

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  15. Show that the set of all x for which log(1+x) le x is equal to [0, in...

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  16. Compute the value of theta the first mean value theorem f(x+h) =f(x) ...

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  17. Show that x^(n)-a=0 has at most one real positive root if n is a posit...

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  18. Show that the function f' if it exists in an interval, can not have an...

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  19. Verify the Lagrange's theorem for the following functions: (a) f(x)...

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  20. Find the value of c, of mean value theorem.when (a) f(x) = sqrt(x^(2...

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