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

2 Answers
Mar 27, 2017

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#.

Mar 27, 2017

#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]}