# Infinit limit

1. Jan 24, 2009

### hockeyfghts5

1. The problem statement, all variables and given/known data

$$\frac{x}{x-5}$$

$$lim x\rightarrow\infty$$

2. The attempt at a solution

$$\frac{x}{x-5} \equiv \frac{1}{1-\frac{5}{x}}$$

$$lim x\rightarrow\infty$$

how do i know what to plug into x to solve the problem. by the way it equals 1

2. Jan 24, 2009

### Staff: Mentor

You don't have to plug anything into x. As x gets larger and larger, what does 1/(1 - 5/x) approach? Can you convince yourself that this expression gets closer and closer to 1 the larger x gets?

3. Jan 24, 2009

### hockeyfghts5

so would you just plug zero for x and the simplify the problem which would give 1?

4. Jan 24, 2009

### jgens

Perhaps to elaborate slightly on what Mark44 has posted: At this moment in time consider lim (x -> infinity) 1/x. We want to find what 1/x approaches as x becomes arbitrarily large. Let us first consider x = 10, then our expression becomes 1/10 = 0.1. Now suppose x = 100, then our expression becomes 1/100 = 0.01. Now suppose x = 100000, than our expression becomes 1/100000 = 0.00001, and for even larger x the expression becomes even smaller; hence, the limit aproaches 0.

Edit: You would not let x = 0, you may let the expression 5/x approach zero as x tends to inifinity though.

5. Jan 24, 2009

### hockeyfghts5

Thanks, that makes sense.