 Hello and welcome to the session, let's discuss the following question. It says evaluate limit x approaching to 0 of e to the power x minus 1 upon under the root 1 minus cos x. So let's now move on to the solution. We have to find the limit of x approaching to 0 e to the power x minus 1 upon under the root 1 minus cos x. Now this is n equal to limit x approaching to 0 of e to the power x minus 1 upon under the root 1 minus cos x is 2 sine square x by 2. As we know that 1 minus cos 2 theta is equal to 2 sine square theta. So here theta is 2 theta is x. So then this is equal to limit x approaching to 0 of e to the power x minus 1 upon under the root 2 sine x. Now we know that limit theta approaching to 0 of sine theta upon theta is 1 and since here we have sine x by 2 so we need to multiply this by x by 2. So we have limit x approaching to 0 of e to the power x minus 1. We take 1 by root 2 outside the limit. So we have sine x by 2 upon x by 2 into x by 2. Again this can be written as 1 by root 2 limit x approaching to 0 of e to the power x minus 1 upon x by 2 into 1 upon sine x by 2 upon x by 2. So again this is equal to 1 by root 2 limit x approaching to 0 of 2 into e to the power x minus 1 upon x into 1 upon sine x by 2 upon x by 2. Now here we will use the limit theta ending to 0 of sine theta upon theta is 1 and also limit x approaching to 0 of e to the power x minus 1 upon x is 1. So this becomes 0. So applying the limit we have 1 by root 2 into 2 into 1 upon 1 this is equal to 2 by root 2 which is equal to root 2. So the value of the limit is root 2. This completes the question and the session. Bye for now. Take care. Have a good day.