Question

can someone help me with the limit:
lim as x approaches2 of: (sqrt x^2-4x+4)/(x-2)

Answer 1

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

Answer 2

could soemone type it out for me, thanks.

Answer 3

Factor the top giving:
\[\lim_{x \rightarrow 2} \frac{\sqrt{(x-2)^2}}{x-2}=\lim_{x \rightarrow 2}1=1\]

Answer 4

dont we get some absolute value type thing, like the (x-2) is actually + or - (x-2)

Answer 5

Only if you take a sqrt, but since it is already there you use the sign convention in the problem. If it was +/- then the limit MIGHT not exist. (I.e., it would approach two different values)

Answer 6

this limit be undefined

Answer 7

this limit be undefined

Answer 8

you are taking
\[\lim_{x->2}\frac{|x-2|}{x-2}\]

Answer 9

how is it undefined?

Answer 10

because your function is
\[ f(x) = \left\{
\begin{array}{lr}
1 & : x >2\\
-1 & : x <2
\end{array}
\right.
\]
and the limit at 2 does not exist since the right hand limit is not equal to the left hand limit

Answer 11

see, i knew it

Answer 12

oh yes. i see you stated that above. good work.

Answer 13

when we take sqrt of (x-2)^2, we end up with absolute value of (x-2), which could either be + or -(x-20

Answer 14

right. the function is exactly what you said, which translates into the piece-wise function that i wrote above.

Answer 15

thank you

Answer 16

could you help me with the other question i posted regarding simplifiying?

Answer 17

it is just like the usual example of
\[\frac{|x|}{x}\] which has no limit at 0
yw

Answer 18

back in ten minutes then i will look

Answer 19

k