Tuesday, 2 April 2019

calculus - Why does the following limit give two answers?

I want to calculate



limt0t2sin2(t)



and I proceed as follows



H=limt02t2sin(t)cos(t)limt02tsin(2t)




and when evaluated gives



H=limt022cos2(t)2sin2(t)=1



But evaluating the other equivalent term gives



H=limt022sin(2t)cos(2t)



and that does not exist as the left hand and right hand limits are not equal.




So, what do you think?

No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...