This is the question once our Maths teacher asked during the coaching and he turned towards me and asked me,’Amrita, I hope you know this!’.It was like nobody answered it,and then it was my turn. Hmmm I thought for a while and said “Yes Sir it is!”. He then asked me to go on and explain how. I said that any function is continuos or not we have to check this in its domain. As the square root’s domain is [0,infinity) because the square root of a negative number is undefined!! Then I said as we have to check the value , we will only consider the right hand limit and not the left hand in case the limit tends to zero.
I also gave the reference of the Maths Book by G N Berman. Oh God the teacher was really impressed and said Good Work Amrita!! And I was very happy to listen that. He then turned to the whole class and said that this was the question that he was trying to get the answer from many books but he was not getting it exactly. During a seminar in IIT Roorkee he consulted few of the professors of IIT and one of them Mr. Gulathi explained him about this fact that in case the limit tends to zero then we only consider the domain in which the given function is defined and hence the square root of a function is continuos. When I listened this I was feeling like jumping and saying”Yes!!”. But i controlled and it was the best day of my life.
Happy to share this with you all!! Cheers 🙂