Show that if xn rightarrow infinity and yn rightarrow y e R

Show that if x_n rightarrow + infinity and y_n rightarrow y e R then y_n/x_n rightarrow 0. What can you say about x_n Y_n?

Solution

A)

Xn---> + Infinity

Yn----> y

Yn/Xn= Limit(x--->+infintity) (Yn/Xn)

= y/Infinity ( As we know Constant/Infinity=0)

Yn/Xn =0

B)

Xn*Yn =Limit(x--->+infintity) (Yn*Xn)

=y*(Limit(x--->+infintity) (Xn)

=y* Infinity

Xn*Yn = Infinity (But y should not be equals to Zero)