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Verify Rolles theorem for function f(...

Verify Rolles theorem for function `f(x)=log(x^2+2)-log3` on `[-1,\ 1]`

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Let `f(x)=\log (x^{2}+2)-\log 3`
Clearly `f `is continous on` [-1,1] `and
`f` is derivable on `(-1,1)`
...
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RD SHARMA-MEAN VALUE THEOREMS-Solved Examples And Exercises
  1. Verify Rolles theorem for function f(x)=sin3x on [0,\ pi]

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  2. Verify Rolles theorem for function f(x)=e^(1-x^2) on [-1,\ 1]

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  3. Verify Rolles theorem for function f(x)=log(x^2+2)-log3 on [-1,\ 1]

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  4. Verify Rolles theorem for function f(x)=sinx+cosx on [0,\ pi//2]

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  5. Verify Rolles theorem for function f(x)=2sinx+sin2x on [0,\ pi]

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  6. Verify Rolle's theorem for function f(x)=x/2-sin((pix)/(6)) on [-1,\...

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  7. Verify Rolles theorem for function f(x)=(6x)/pi-4\ s in^2x on [0,\ ...

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  8. Verify Rolles theorem for function f(x)=4^(sinx) on [0,\ pi]

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  9. Verify Rolles theorem for function f(x)=x^2-5x+4 on [1,\ 4]

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  10. Verify Rolles theorem for function f(x)=sin^4\ x+cos^4\ x on [0,\ pi...

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  11. Verify Rolles theorem for the function: f(x)=sinx-sin2x on [0,\ pi]

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  12. Using Rolles theorem, find points on the curve y=16-x^2 , x in [-1,\...

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  13. At what points on the curve y=x^2 on [-2,\ 2] is the tangent parall...

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  14. At what points on the curve y=e^1-x^2 on [-1,\ 1] is the tangent pa...

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  15. If f:[-5,\ 5]->R is differentiable and if f^(prime)(x) doesnt vanis...

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  16. It is given that the Rolles theorem holds for the function f(x)=x^3...

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  17. Verify Lagrange's mean value theorem for the function f(x)=(x-3)(x-6...

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  18. Verify Lagranges mean value theorem for f(x)=x(x-2) on [1,\ 3] on t...

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  19. Verify Lagranges mean value theorem for f(x)=x-2sinx on [-pi,\ pi]

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  20. Verify L.M.V. theorem for f(x)={2+x^3, xlt=1 3x , x >1 on [-1,2]

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