1. ## critical limit problem

hi
well................ this is my first thread on this site

my name is mohamed and iam at engineering faculty first grade well i was solving an excersise preparing for my next week exam and i found tough proble i spent hours trying to solve it but i failed i wish if any one can help me here he problem is

lim [lnX - 1]/X - e
X tends to "e"

and something else can any one help me howto write maths sympols here excuseme i dont do on forums alot

thxxxxxxx

2. Originally Posted by mohamedsafy

hi

well................ this is my first thread on this site

my name is mohamed and iam at engineering faculty first grade well i was solving an excersise preparing for my next week exam and i found tough proble i spent hours trying to solve it but i failed i wish if any one can help me here he problem is

lim [lnX - 1]/X - e

X tends to "e"

and something else can any one help me howto write maths sympols here excuseme i dont do on forums alot

thxxxxxxx
This is an application of the derivative

$f'(c)=\lim_{x\to{c}}\frac{f(x)-f(c)}{x-c}$

So in your case $f(x)=\ln(x)$, $c=e$ $f(c)=\ln(e)=1$

So

$\lim_{x\to{e}}\frac{\ln(x)-1}{x-e}=\left(\ln(x)\right)'\bigg|_{x=e}=\frac{1}{e}$

3. ## thxxxxx

thxx alot that was sooo helpful