Question

What is `lim_(xrarroo) 1/x`?

Answer 1

By direct substitution:
`lim_(x->oo)1/x=0`

Explanation:

Logically, imagine the value of the denominator of a fraction increasing. For example: `1/10>1/11>1/12>1/(10,000)`.

This shows that (if the numerator is a constant like above) as the denominator of a fraction increases, the value of the fraction approaches `0`.

Answer 2

`lim x->oo 1/x = 0`

Explanation:

You need to realize that limit is a `y`-value.

Divide the numerator and denominator by the largest `x`-term
`lim x-> oo (1/x)/(x/x) = lim x-> oo (1/x)/1 = 0`

From the graph `f(x) = 1/x` you can see that when `x` is large, `y-> 0`: graph{1/x [-4.295, 15.705, -5, 5]}