# How to find #lim(ln(2x)/(2+x)) x-> # infinity?

##### 2 Answers

The limit equals

#### Explanation:

Since we are of the form

#L = lim_(x->oo) (2/(2x))/(1)#

#L = lim_(x->oo) 1/x#

This is now a recognizable and commonly seen limit.

#L = 0#

Hopefully this helps!

#### Explanation:

Logarithmic functions grow slower than polynomial functions. Polynomial functions grow slower than exponential functions.

Since

Thus, the denominator will outpace the numerator and as

Note what would happen if the fraction were inverted:

#lim_(xrarroo)ln(2x)/(2+x)=0#

#lim_(xrarroo)(2+x)/ln(2x)=oo#