Help on Limit Problem?

Question

My book says the answer to the problem below is -1, but I keep getting just 1. Can someone show me step by step how to do the problem below. If the answer is just 1..you can just say my book problem put the wrong answer on accident.

Find the limit as h approaches 0 for the function :
(1/(1+h)-1)/ h

Answer 1

The given expression should be interpreted like this:

1
------- - 1
1 + h
-------------
h

If we get a common denominator, then we have

1 - (1 + h)
--------------
1 + h
-----------------
h

or

1 - 1 - h
-----------
(1 + h) h

-h
-----------
(1 + h) h

-1
-------
1 + h

which goes to -1 as h goes to 0.

Answer 2

Here are the steps to do this question:
1. (1/(1+h)-1)/ h
2. (1-(1+h)/1+h)) * [1/h] Find the common denominator which is 1+h. Therefore, you multiply the top by 1+h.
3. [(1-1+h)/(1+h)] *[1/h] Add the like terms which are 1-1=0, then you are left with -h which can be divided by the h that was inverted. Now you will be left with a -1 on top.
4. [-1/1+h] As h goes to 0
5. -1/1 = -1

Answer 3

Ti-89 did give the answer as -1.

Here is my solution

lim(1/(1+h)-1)/h=lim(1/(h*(1+h)) - lim(1/h)

First lim is 0 as h approaches 0
Second lim is 1 as h approaches 0
So the answer is 0-1 = -1

By the way, nice no'n la'. Vietnam ha?

Answer 4

Multiply it by (1+h)/(1+h) to get
(1 - (1+h))/(h+h^2) = -h/(h+h^2)
multiply by (1/h)/(1/h) to get
-1/(1 + h)
lim h→0 -1/(1 + h) = -1