Question

Limits with an absolute value.

Answer 1

\[\frac{ 2x-6 }{ |x-3| }\]

Answer 2

lim
x->3^-

Answer 3

heya @hartnn !

Answer 4

hi :)
have u solved such sums before ?

Answer 5

so basically, our teacher has us plug in the limit and see if it works, in this case, I get 0/0

Answer 6

ok, first take out 2 common in numerator, what do u get ?

Answer 7

\[2\frac{ x-3 }{ |x-3| }\]

Answer 8

right.
now before cancelling x-3 from numerator and denominator
u need to find whether it is +1 or -1
denominator is always positive because of |...|
what about numerator?
positive or negative ?

Answer 9

negative because 2.9(2)-6 is negative

Answer 10

idk what was that but,
numerator is negative because x-> 3-
so x is very near to 3 but less than 3
so x-3 is negative.
got this ?

Answer 11

ya would it make sense if I plugged in 3^- and got 6^-1 - 6 and left a ^- on top?

Answer 12

denoting negative, or is that dumb?

Answer 13

so the fraction will be
(x-3)/ |x+3| = -1
so the limit = 2/(-1) = -2
got this ?

Answer 14

(x-3)/ |x-3| = -1

Answer 15

ahhh

Answer 16

nice, thanks alot @hartnn !!

Answer 17

welcome :)