Doubt from functions

ques 51 ans is d @Ajay_2020_1 @Satyendra_2019 @Sneha_2021 @akash_2020 and anyone


@Venkat_2020 bro see this one too

Ques 67 ans is D

ques 59 ans is d

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.

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

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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 ?


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