# Limit ln function + ln rules

1. May 22, 2010

### oswald88

1. The problem statement, all variables and given/known data

Find limit lim x->0+ of lnx+1/x

2. Relevant equations

1/x = ln e^1/x

3. The attempt at a solution

ln x + ln e^1/x = ln x*e^(1/x)
lim x-> 0+

ln x + ln e^1/x = ln 0*inf = ln 0 = - inf
lim x-> 0+

Source: my self vs http://www.numberempire.com/limitcalculator.php

#### Attached Files:

• ###### 2b.gif
File size:
1.1 KB
Views:
76
Last edited: May 22, 2010
2. May 22, 2010

### oswald88

Re: Limit ln function + ln rules - Wolfram Mathematica answers...

above, pitcure of mathematica solution..

#### Attached Files:

• ###### a.gif
File size:
12.2 KB
Views:
113
3. May 22, 2010

### gabbagabbahey

$$\lim_{x\to x_0} f(x)g(x)=\left(\lim_{x\to x_0} f(x)\right)\left(\lim_{x\to x_0}g(x)\right)$$

The above property is only true if both the individual limits exist (are finite). But, $$\lim_{x\to 0^+}e^{1/x}=\infty[/itex] which isn't finite, and so you can't claim that [tex]\lim_{x\to 0^+}xe^{1/x}=\left(\lim_{x\to 0^+}x\right)\left(\lim_{x\to 0^+}e^{1/x}\right)=(0)(\infty)=0$$