76 957
Assignments Done
Successfully Done
In June 2019

Answer to Question #18352 in Real Analysis for Matthew Lind

Question #18352
Using the definition of the limit at infinity verify that
0 does not equal lim x-->infinity cosx.
Expert's answer
The assumption
limx-->infinity cosx = 0
means that for any epsilon>0 there exists N>0 suchthat for all x>N we have that
|cos x| < epsilon.
Consider the seuqence of numbers x_n = 2 pi n.
lim x_n = +infty
cos x_n = 1 for all n.
Take epsilon < 1.Then for any N>0 there exists n such that
x_n = 2 pi n >N
cos x_n = 1 >epsilon.
Therefore 0 does not equal lim x-->infinity cosx.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!


No comments. Be first!

Leave a comment

Ask Your question

Privacy policy Terms and Conditions