Question

Could someone help me evaluate this limit?

`lim _(x->oo)(x+9)/(x-9)`

Answer 1

`1`.

Explanation:

We have,

`lim_(x rarr oo) ((x + 9)/(x - 9))`

Let's Assume that `y = 1/x`. So, `x = 1/y`.

Now, If `x rarr oo` then, `y rarr 0`.

So, We get,

`lim_(y rarr 0) ((1/y + 9)/(1/y - 9)) = lim_(y rarr 0)(((1 + 9y)/y)/((1 - 9y)/y)) = lim_(y rarr 0) ((1 + 9y)/(1 - 9y))`

Now, you can put `y = 0` and find the limit.

So, The Final Limit is `= ((1 + 9 * 0)/(1 - 9* 0)) = 1/1 = 1`

Hope this helps.