Evaluate the limit, if it exists.

hey guys, so I'm doing some limit questions, and I'm kind of stuck on one, and it's a even number so I have no solution for it in the book onto how to do it, but anyways this is what I have for this question so far.

Question:

lim (3+h)^{-1}-3^{-1}/ h

h ->0

Ok so this is what I've done so far,

lim 1/(3+h) - 1/3 all divided by h

h ->0

lim 3-(3+h)/3(3+h) all divided by h

h ->0

lim 3-3-h/9+3h * 1/h

h ->0

lim 3-3-1/9+3h (cancelled the h's)

h ->0

Plug in the 0s where the h is -1/ 9+3(0) = -1/9,

Not sure if this is correct or not, and I think I may have made a mistake somewhere, please correct me if so.

Thank you, sorry if the format isn't as good, I think some of you know I'm terrible with that stuff lol.

Re: Evaluate the limit, if it exists.

Quote:

Originally Posted by

**Oldspice1212** Question:

lim (3+h)^{-1}-3^{-1}/ h

h ->0

Ok so this is what I've done so far,

lim 1/(3+h) - 1/3 all divided by h

h ->0

lim 3-(3+h)/3(3+h) all divided by h

h ->0

lim 3-3-h/9+3h * 1/h

h ->0

lim 3-3-1/9+3h (cancelled the h's)

h ->0

Plug in the 0s where the h is -1/ 9+3(0) = -1/9,

All of that is correct except that. We never never **plug in** when doing limits.

That is a completely wrong way to think about limits.

What happens to $\displaystyle \frac{(3)-(3+h)}{3h(h+3)}$ as $\displaystyle h\ne 0~\&~x\sim 0~?$

That is, h is 'close to' but not equal to zero. Unless that is clear to you then you will have trouble later on in mathematical proofs.

Re: Evaluate the limit, if it exists.

Quote:

All of that is correct except that. We never never plug in when doing limits.

That is a completely wrong way to think about limits.

What happens to as

That is, h is 'close to' but not equal to zero. Unless that is clear to you then you will have trouble later on in mathematical proofs.

You are absolutely correct, I actually knew that, I'm just so used to saying "plug it in", thanks a ton for the clarification.