 Hello and welcome to the session. In this session we discussed the following question which says, evaluate limit x times 2 pi by 2 root 2 minus root 1 plus i max with n upon root 2 into cos square x. Before moving on to the solution, let's discuss the hospital room according to which we have that if s of a upon g of a is of the form 0 upon 0 or infinity upon infinity then limit x times 2 a upon g of x is equal to limit upon g dash x is the key idea that we would use in this question. We are supposed to find the limit, limit x times 2 pi by 2 and this one upon root 2 root 2 minus square root of and this one upon i by 2 this would be equal to root 2 minus 1 plus 0 that is equal to 0 upon 0. For this we would have limit x times 2 a fx upon gx is equal to limit x times 2 a f dash x upon g dash x. The required limit would be equal to limit 0 upon d by dx is equal to limit x times 2 pi by 2. Now d by dx of root 2 would be 0 minus d by dx root of 1 plus i max would be half d by dx of sin x which is which would be root 2 into this is equal to limit cancels this is equal to we get this is equal to 1 by 1 plus sin pi by 2 root of 1 plus 1 into 1 that is sin pi by 2 is 1. So further this is equal to 1 by 2 into root 2 or you can say 1 by 8 that is limit x times 2 this one upon is equal to 1 by 8 session hope you understood the solution of this question.