Thread: Limits

Help me solve this please:

lim [(x+1)^2 - 1] / x
x-> 0



I got 0. I don't think that's right though.

Originally Posted by habibixox

Help me solve this please:

lim [(x+1)^2 - 1] / x
x-> 0



I got 0. I don't think that's right though.

Start by expanding the numerator and collecting like terms, then dividing each term by , before trying to let ...

(x+1)(x+1) - 1 / x

what i did was:

Lim lim [x+1] ^2 - lim 1 / lim x
x-> 0 x->0 x->0 x-> 0

Originally Posted by habibixox

(x+1)(x+1) - 1 / x

what i did was:

Lim lim [x+1] ^2 - lim 1 / lim x
x-> 0 x->0 x->0 x-> 0

Obviously what you have done is not working, since you are getting 0/0, an indeterminate form. Why not try following the advice you were given?

i got 2.

Originally Posted by habibixox

i got 2.

Would you mind showing how you got an answer of 2 please?

(x+1) (x+1) =
x^2+2x+1 -1 / x

then
x(x+2) / x

then cancel the x's

0 +2 = 2

Originally Posted by habibixox

(x+1) (x+1) =
x^2+2x+1 -1 / x

then
x(x+2) / x

then cancel the x's

0 +2 = 2

Assuming you meant (x + 1)(x + 1) + 1 = x^2 + 2x + 1 - 1 then you are correct Well done.

thank you!
so ultimately there are only three ways of solving limits

by factoring
substitution
and conjugation
right?

and you only use conjugation when there is a square root right and a number?

Originally Posted by habibixox

thank you!
so ultimately there are only three ways of solving limits

by factoring
substitution
and conjugation
right?

and you only use conjugation when there is a square root right and a number?

There are many more ways than three to solve limits. The easiest way is to find some way to simplify the function so that you can factor and cancel any terms that will end up making an indeterminate form, which like you said, might involve factoring or conjugation.
Substitution is only used if the function is continuous at the point you are approaching, or once you have done enough to be able to substitute without resulting in an indeterminate form.