# Doubt from AOD

Infinity for 42. Nice use of rolles theorem

C for 53?

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Q42) logically Since xsin(π/x) is a oscillatory function hence we will get infinite tangents of zero slope

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Yeah i thought the same way… But i wanted to know how to use Rolle’s theorem in this question…

Sorry bro, wasnt online for some days.

Notice that at 1/integers, the function becomes zero.

Apply rolles theorem.

Between 0 and 1 infinite pairs of the type like (1/2,1/3) can be formed and thus infinite is the amswer

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For 53 you need to analyse the derivative.

The two points where derivative is zero should be opposite in sign. Use this fact and try again. I dont have the solution written now and I am too lazy to write again lol

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Thanks bro…

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