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

1 Answer
Alexander
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]}

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