limits

[RobinBrock24]

Cant figure out how to get this problem started. I have to simplifiy the problem first before I figure the limit
Can anyone help me get started on this.


(3^x - 1) / x

 

[tkhunny]

Limits need a target. Where is this one going?

 

[Pklarreich]

Limits need a target. Where is this one going?

If you have lim[x -> h], you just have (3^h - 1) / h, which is no fun unless h = 0. [I suppose that's part of the problem -- first figure out what the problem is, then solve it.]

So I am sure that is the value of h.

Now you want
3^h - 1
lim --------- =
a->0 h

3^h - 3^0
lim -----------
a->0 h

Look familiar? That's the derivative of 3^x at x = 0, isn't it?

And D3^x = 3^x ln 3

At x = 0, that's ln 3.