By using squeezing theorem we can prove that
limxsin (1/x) = 0
x -->0
Why couldn’t we have the same result by writing
limxsin (1/x)= limx.limsin (1/x)=0.limsin (1/x)=0 ?
x -->0 x-->0 x -->0
Thanks for ur help
Anonymous
Favorite Answer
First off, can you prove that the limit of a product is the product of the limits?
Secondly, the limit as x approaches 0 of sin(1/x) is not 0. As x approaches 0, 1/x increases without bound. As it does so, the sine continues to oscillate between -1 and 1, and never approaches a limit. So, even if you can do the proof I mentioned, you're left with the question of what you get when you multiply zero by something which does not exist.