Infinite Limit: Solving \frac{x}{x-5}

[hockeyfghts5]

Homework Statement

<br /> \frac{x}{x-5}<br />

<br /> lim x\rightarrow\infty<br />2. The attempt at a solution<br /> \frac{x}{x-5} \equiv \frac{1}{1-\frac{5}{x}}<br />

<br /> lim x\rightarrow\infty<br />

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

 

[Mark44]

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?

 

[hockeyfghts5]

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

 

[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.

 

[hockeyfghts5]

Thanks, that makes sense.