Please help me with this problem

Suppose f(x)->- and g(x)-> +- as x->+inf. find example of functions f and g with there properties and such that:

8. Suppose f (x) - 0 and g(x) - too as x - too. Find examples of functions f and g with these properties and such that: a. lim If (x) . g(x)] = too x- + 00 Prover (choose the functions): Explainer (check the limits): f (x) = lim f (x) = x - + 00 g (x) = lim g(x) = x- +00 f ( x) . g(x) = lim [f (x) . g(x)] = x -+ + 00 b . x - + 00 lim If (x) . g(x)] = -0o Prover (choose the functions): Explainer (check the limits): f (x) = lim f (x) = x - + 0o g (x) = lim g(x) = x - + 00 f (x) . g(x) = lim [f (x) . g(x)] = x - + 00 c. lim [f (x) . g(x)] = A, where A is any arbitrary real number that you choose yourself. Prover (choose the functions): Explainer (check the limits): f (x ) = lim f (x) = x - + 00 g (x ) = lim g(x) = x - + 00 f (x) . g(x) = lim [f (x) . g(x)] = x - + 00d. Think carefully about what the symbols co, -co and 0 represent in the statements f (x) - 0 and g(x) - too. (Hint: Are they fixed values, or do they describe a particular behavior?) Now use your work from parts a-c to explain why 0 . too is an indeterminate form. e. Thinking carefully again about the meaning of the symbols co and -co, explain how this is different from the determinate forms too . too and a . too (where a # 0)