# Need help on proof

1. Dec 13, 2003

### fangtu

Hi I need help again on my assignment, it's kindda hard...I did do what I could but I can't come up with anything@@" please help
***********
Let F(x)=ln(x). We know that F'(x)=1/x. We will use this fact and the definition of derivatives to show that lim(n->inf) (1+1/n)^n=e
a) Use the definition of the derivative to show that
f'(1)=lim(h->0)(ln(1+h)/h)

b)Show that (a) implies that
ln[lim(h->0)(1+h)^1/h]=1

c) Set h=1/h in (b) and let n-> inf Show that this implies
lim(n->inf) (1+1/n)^n=e

2. Dec 13, 2003

### himanshu121

Apply the ab initio Rule for Derivative

put x=1
u will get first part

now F'(1)=1/x=1

u will get second part

Set h=1/h in (b) and let n-> inf will give u
third part of Q

3. Dec 13, 2003

### fangtu

uhmmm...don't I suppose to "show" everything through a process until it reaches the final answer somewhat like a proof? cuz that's the way I understand the problem@@"

4. Dec 13, 2003

### himanshu121

Yes u have to

its just hint which u yourself has quoted

Anyway give your attempt as u will be giving in assignment

5. Dec 13, 2003

### fangtu

uhmm....I did, but still don't know how....thanks anyways..I'll be discussing with my classmates thank you