what are some theory's about limits that help explain how you can determine the limit as x approaches infinity?

This is to help me understand a part in my project because I'm having a hard time understanding how this works.

It asks for three equations. one that approaches infinity, one that approaches zero, and one that approaches any number that is not zero.

I chose the equationsf(x)=limx4x+2= , f(x)=limx2/x=0, and f(x)=limx(1/x)+5=5.

so, any explanation on how it works in theory would help.