Infinity for 42. Nice use of rolles theorem
C for 53?
Yes…right… Please show your solution…
Bro please send your solution na… @manan_uppadhyay
Q42) logically Since xsin(π/x) is a oscillatory function hence we will get infinite tangents of zero slope
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
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