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:
$\displaystyle \lim_{x \to 0} \frac {\frac {-x}{x + 1}}x$
now what?
"easy" way: realize that this is the derivative of $\displaystyle \frac 1x$ at $\displaystyle x = 1$. (of course, the x here would usually be "h" in the formula, but that doesn't matter)
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)
that is correct
no worries.(sorry i dont know how to do the math codes or anything. i just have to use the underline and stuff lol)
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!