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CMI 2023 | Data Science | Part B | Question: 6

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lim(x->inf) [x(1 - cos(1/root(x)))]

Let, x = 1/t...!!
As x--> infinite... So, t-->0

Hence,
lim(t-->0) [ (1/t) .(1 - cos(root(t)) )]
= >>By applying L'Hospital rule...
lim(t-->0) sin(root(t)) / {2root(t).1}
= 1/2 . lim(t-->0){sin(root(t)) / root(t)} 

We know that..
at x tending to 0, sinx/x = 1..
So, the ressult will come out to.."
1/2 x 1
= 1/2 = 0.5

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