How do you find the limit of (x/(x-3)) as x approaches oo?

1 Answer
Jul 18, 2016

lim_(x->∞) (x)/(x-3) = 1

Explanation:

This limit is also known as an infinite limit. In case of a polynomial such as this one, we can divide each term in the expression by the highest power of x.

lim_(x->∞) (x)/(x-3) = lim_(x->∞) (x/x)/(x/x-3/x) = lim_(x->∞) (1)/(1-3/x)

Since we know that lim_(x->∞) 1/x = 0, we can now solve this last limit.

lim_(x->∞) (1)/(1-cancel(3/x)) = (1)/(1-0) = 1

By graphing the function itself, we can also determine that the value approaches 1 as shown below.

graph{(x)/(x-3) [-10, 10, -5, 5]}