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If f(x) =log x find all numbers strictly...

If f(x) =log x find all numbers strictly between `e^(2)` and `e^(3)` such that `f'(x) = (f(e^(3))-f(e^(2)))/(e^(3)-e^(2))`

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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (3)
  1. Verify Rolle's theorem for the following function f(x) = 2x^(3) + x^(2...

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  2. Verify Rolles theorem for the function: f(x)=x(x+3)e^(-x//2) on [-3...

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  3. Show that there is no real number p for which the equation x^2 -3x + p...

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  4. Verify Rolle's theorem for the function f(x) = x^(2) in the interval [...

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  5. Verify the Rolle's theorem for the functionf(x) = x^(2) - 3x+2 ...

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  6. If a+b + c = 0, then show that the quadratic equation 3ax^(2) + 2bx +c...

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  7. Discuss the applicability of Rolles theorem for the function f(x)=x...

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

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  9. Discuss the application of Rolle's theorem to the function f(x) = log ...

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  10. Verify Rolle's theorem for the function f(x) = x^(3) -6x^(2) + 11x-6 i...

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  11. Verify Rolle's Theorem for the function f(x)= 10x - x^(...

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  12. Find 'c' of the mean value theorem, if: f(x) = x(x-1) (x-2), a=0, b=...

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  13. If f(x) =log x find all numbers strictly between e^(2) and e^(3) such ...

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  14. Separate the intervals in which the polynomial 2x^(3) -15x^(2) + 36x+1...

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  15. Use the function f(x)=x^(1/x),x >0, to determine the bigger of the two...

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  16. Show that Lagrange's mean value theorem does not holdior the function ...

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  17. Verify Lagrange's mean yalue'theorem for the function f(x) = sin x in ...

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  18. If f'[x) exists for all points in [a,b] and (f(c ) -f(a))/(...

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  19. If f(x) = (x-1)(x-2) and a = 0, b = 4, find 'c' using Lagrange's mean ...

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  20. Examine if Mean Value Theorem applies to f(x) = x^(3) + 3x^(2) - 5x i...

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