Calculus!!! HELP!!! T_T Give examples of functions f(x) and g(x) with:?

Question

Give examples of functions f(x) and g(x) with lim f(x) as x approaches infinity = infinity, lim g(x) as x approaches infinty = infinity, and
a) lim ((f(x))/(g(x))) as x approaches infinity = infinity
b) lim ((f(x))/(g(x))) as x approaches infinity = 6
c) lim ((f(x))/(g(x))) as x approaches infinity = 0
d) Is it possible to have lim ((f(x))/(g(x))) as x approaches infinity = -1? Wither give an example or explain why it is not possible.

I have no idea where to even start this. Any help would be greatly appreciated.

Answer 1

a) f(x) = x^2; g(x) = x

b) f(x) = 6x; g(x)=x

c) f(x) = x; g(x) = x^2

d) f(x) = -x; g(x) = x

there are many other functions that could give these limits (like sin x and -x for part d)), but these should work for your examples

Answer 2

Try playing with these for f(x) and g(x)...

x
x^2
6x

And consider, what kind of number do you get when you divide a positive number by a positive number?