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Hi, I am in a first semester Calculus I course in college with an intermediate skill level with precalc and a basic understanding of limits and infinity. I do not understand how to solve this problem I attempted to do so only to find out after completion that ∞/∞ is indeterminate rendering my solution void.

Suppose f(x) →0 and g(x) → 0 as x → +∞. Find examples of functions f and g with these properties and such that:

a. lim

Here is my attempt

Let f(x) = 1/x and g(x) = (1/x)+1

lim

## Homework Statement

Suppose f(x) →0 and g(x) → 0 as x → +∞. Find examples of functions f and g with these properties and such that:

a. lim

_{x→+∞}[itex]\left[\frac{f(x)}{g(x)}\right][/itex] = + ∞## The Attempt at a Solution

Here is my attempt

Let f(x) = 1/x and g(x) = (1/x)+1

lim

_{x→+∞}[itex]\left[\frac{\frac{1}{x}}{\frac{1}{x}+1}\right][/itex]= [itex]\frac{1}{x}[/itex] * [itex]\frac{x}{1}+1[/itex] = ∞ + 1 = + ∞
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