lim (4-v)/abs(4-v) as v-4

Just need to confirm if i'm right.

Is it going to be lim (4-v)/(4-v) as v-4^+
and lim (4-v)/(v-4) as v-4^- ?

Question

lim (4-v)/abs(4-v) as v->4

Just need to confirm if i'm right.

Is it going to be lim (4-v)/(4-v) as v->4^+
 and lim (4-v)/(v-4) as v->4^- ?

amistre64 · Answer

as v approaches 4, this is the same as saying:

4-v
---  ; which is a removable discontinuity
4-v

amistre64 · Answer

http://www.wolframalpha.com/input/?i=%284-v%29%2F%7C4-v%7C that aint a nice looking graph is it

amistre64 · Answer

one way approaches 1 and the other way approaches -1; so a limit does not exist

anonymous · Answer

yes but it approaches 4 from the left and right. Wouldn't it be 
                                                                                                4-v
                                                                                               ---- as it approaches from the left?                                                                                  v-4

amistre64 · Answer

yes; which is removable as well and we are left with -1

amistre64 · Answer

since the limit is not the same from both directions; it does not exist

anonymous · Answer

ok thanks..Just thought I'd make sure

amistre64 · Answer

when in doubt, its always best to make sure :)  good luck