# How to show that the limit is 0?

We are given the following: $$w_s - w_u(2+r) - (1+r)h \geq 0 \tag{1}$$ where $$h$$ is positive.

Now, consider the following fraction: $$f = \frac{w_u(2+r) + (1+i)h - w_s}{i - r}$$

The condition for the entire fraction to be positive (assuming $$i > r$$) is:

$$w_u(2+r) + (1+i)h - w_s \geq 0 \tag{2}$$

Combining (1) and (2) leads to the following:

$$(i-r)h \geq 0$$ which leads me to think that $$f = 0$$ when $$(i-r) = 0$$.

However, I am having trouble proving this formally, since if $$i=r$$, the fraction is undefined. I am unsure how to take the limit of this (applying L'Hopital's rule did not yield the result).

How do I show formally that $$f \to 0$$ as $$i \to r$$?