Sandwich Theorem

Question

Use the sandwich theorem to find the limit of {(cos(n))/(10n^2)}

Answer 1

Since 0 <= cos(n) <= 1, therefore

 

0/(10n^2) <= cos(n)/(10n^2) <= 1/(10n^2)

 

Now, find the limits to the sequences on the left and right:

 

lim {0/(10n^2)} = lim{0} = 0

 

lim{1 / (10n^2)} = 0

 

Therefore, the sandwich theorem holds that the limit of cos(n)/(10n^2) is also 0.