# Thread: quick help

1. ## quick help

i need help with starting this problem

find the limit of the following as x---> 0

[1/(x+1)]-1
x

2. Originally Posted by BigPapa
i need help with starting this problem

find the limit of the following as x---> 0

[1/(x+1)]-1
x
hard way (algebraic):

not many algebraic options here, combine the fractions in the numerator, you get:

$\lim_{x \to 0} \frac {\frac {-x}{x + 1}}x$

now what?

"easy" way: realize that this is the derivative of $\frac 1x$ at $x = 1$. (of course, the x here would usually be "h" in the formula, but that doesn't matter)

3. Originally Posted by Jhevon
hard way (algebraic):

not many algebraic options here, combine the fractions in the numerator, you get:

$\lim_{x \to 0} \frac {\frac {-x}{x + 1}}x$
well we havent gotten to derivatives yet so i have to do it algebraicly

4. Originally Posted by BigPapa
well we havent gotten to derivatives yet so i have to do it algebraicly
ok, so finish up. how can you simplify where i left off?

5. ok i think i got it.

from there you multiply the numerator by 1/x and you end up with

-x
x(x+1)

x's cancel

-1
(x+1)

substitute 0 for x and you get

-1

(sorry i dont know how to do the math codes or anything. i just have to use the underline and stuff lol)

6. Originally Posted by BigPapa
ok i think i got it.

from there you multiply the numerator by 1/x and you end up with

-x
x(x+1)

x's cancel

-1
(x+1)

substitute 0 for x and you get

-1
that is correct

(sorry i dont know how to do the math codes or anything. i just have to use the underline and stuff lol)
no worries.

if you are so inclined, you can learn the codes here

if not, just type fractions thusly:

(numerator)/(denominator)

example, you would type your second to last line as (-1)/(x + 1), or simply -1/(x + 1) since there is no ambiguity there.

but please use parentheses wisely. if you had typed -1/x + 1 that would be wrong!

7. ok thanks for your help. i think i might go learn the codes