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  • Help me answer: For which of the following, Rolle's Theorem s applicable in the interval [1, 2] ?

For which of the following, Rolle's Theorem s applicable in the interval [1, 2] ? 

  • Option 1)

    \frac{\sin \pi x}{2x-3}

  • Option 2)

    (x-2)\ln x

  • Option 3)

    [x]

  • Option 4)

    \{x\}

 

Answers (1)

best_answer

As we have learned

Rolle's Theorems -

Let f(x) be a function of x subject to the following conditions.

1.  f(x) is continuous function of    x:x\epsilon [a,b]

2.  f'(x) is exists for every point :  x\epsilon [a,b]

3.  f(a)=f(b)\:\:\:then\:\:f'(c)=0\:\:such \:that\:\:a<c<b.

-

 

\frac{\sin \pi x}{2x-3}  is discontinous at 3/2 

[x] is discontinous at 2 

\left \{ x \right \} is discontinous at 2 

so rolle's theorem is not applicable in above three cases 

But , (x-2) lnx satisfies all three condition of rolle's theorem

 

 

 

 


Option 1)

\frac{\sin \pi x}{2x-3}

Option 2)

(x-2)\ln x

Option 3)

[x]

Option 4)

\{x\}

Posted by

Himanshu

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