Find the indicated limit, if it exists.

Question

anonymous · Answer

attachment

anonymous · Answer

Could somebody please help? @jim_thompson5910

jim_thompson5910 · Answer

look at the first piece

when x = 0, what is the function output?

jim_thompson5910 · Answer

ie...

if x = 0, then 5x - 8 = ???

anonymous · Answer

-8?

jim_thompson5910 · Answer

so that's the left hand limit

when x = 0 for the second piece, we get

|-4 - x| = |-4 - 0| = |-4| = 4

so the right hand limit is 4

jim_thompson5910 · Answer

since the left hand limit and the right hand limit are NOT the same value, this means that the limit at x = 0 does NOT exist

jim_thompson5910 · Answer

and if you were to graph this, you would have a disconnect at x = 0, which gives you visual proof of a limit not existing there

anonymous · Answer

ohhh ok i was doing this totally wrong! thanks so much!

jim_thompson5910 · Answer

yw

anonymous · Answer

would you mind helping me with one more?

anonymous · Answer

Find the indicated limit, if it exists.
@jim_thompson5910

anonymous · Answer

the limit would be 1 right? @jim_thompson5910

zzr0ck3r · Answer

do the left and right handed limits equal each other?

zzr0ck3r · Answer

-handed lol

anonymous · Answer

they equal each other don't they?

jim_thompson5910 · Answer

you are correct, both left and right hand limits are 1

so the overall limit as x--> -8 is 1

anonymous · Answer

because -8 + 9 = 1
and -7 - (-8) = 1

anonymous · Answer

ok thanks! on this one i have no idea what to do.
Use graphs and tables to find the limit and identify any vertical asymptotes of

anonymous · Answer

whoops wrong attachment here is the right one. sorry

jim_thompson5910 · Answer

ok a table may be better

make a table for 1/(x-6) and use the x values that are less than 6 (but are slowly getting closer to 6)

anonymous · Answer

-∞ ; x = 6
-∞ ; x = -6
∞ ; x = -6
1 ; no vertical asymptotes

anonymous · Answer

so would it be the first one?

anonymous · Answer

thos are my answer choices

jim_thompson5910 · Answer

you are correct, the limit is negative infinity and the vertical asymptote is x = 6

anonymous · Answer

do you have time for one last one? sorry! @jim_thompson5910

jim_thompson5910 · Answer

sure

anonymous · Answer

Find the indicated limit, if it exists.

jim_thompson5910 · Answer

make sure the left and right hand limits are equal

anonymous · Answer

it's just like the first two i did but the middle one is throwing me off a little bit

jim_thompson5910 · Answer

don't worry about the middle

jim_thompson5910 · Answer

you can have 2 limits approach a value, but have the point elsewhere

jim_thompson5910 · Answer

ex:

|dw:1370554868689:dw|