Question

how do you find the limit of.......

Answer 1

\[(\frac{ 1 }{ 2+x }-\frac{ 1 }{ 2 })/x\]

Answer 2

as x goes to zero?

Answer 3

yes

Answer 4

do the algebra

Answer 5

yes but 0 cannot be in the denominator

Answer 6

\[\frac{1}{2+x}-\frac{1}{2}=\frac{2-(2+x)}{2(2+x)}=\frac{-x}{2(2+x)}\]

Answer 7

do the algebra first, substitute last

Answer 8

ok

Answer 9

now cancel the \(x\) top and bottom

Answer 10

then you are left with 2x2=4 right?

Answer 11

you see that \[\frac{\frac{1}{2+x}-\frac{1}{2}}{x}=\frac{-1}{2(2+x)}\]\]

Answer 12

oh nevermind

Answer 13

you are left with \(4\) in the denominator, yes, but you have a \(-1\) in the numerator

Answer 14

ok

Answer 15

always works this way
do the algebra first
if you get a zero top and bottom, you will be able to factor and cancel
then substitute

Answer 16

alright thanks so much

Answer 17

yw