# Doubt from functions

For first let x=f(t)

Isi cmi 2019 problem

This can be done by cauchy mean value theorem

But @Venkat_2020 has best approach i m sure motivation of this approach is @Hari_Shankar sir same was done by him in forum.

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Lmvt theoram

- @Achyut_2020 not mine approach but this problem can be solved in 2 or 3 step by knowing one approximation.

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For q52

I assume f(x)=1-x but not getting ans

Is it wrong to assume a function in this type of question?

answer is coming

\frac{1}{2019}

we get ,

{\displaystyle\int}\left(2x-1\right)^{2018}\,\mathrm{d}x

Then the substitution,u=2x-1 will give us the answer as \frac{1}{2019}

@akash_2020

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@Sneha_2021 i face problems in doing such questions in which is LMVT involved. Can you please post some short solution and can you please tell me a good source where i can find such differentiability problems ?

Okay,thanks