Question

Find the indicated limit, if it exists.

Answer 1

you need to find the limit from the left of -1
and from the right of -1
first

Answer 2

can you help me? I don't get this lesson, i don't know how to do that.

Answer 3

for the limit from the left you need to consider f(x)=4-x if x<-1
\[\large \lim_{x\to-1^{-}}4-x=4-(-1)=5\]
for the limit from the right you consider f(x)=x+6 if x>-1
\[\large \lim_{x\to-1^+}x+6=-1+6=5\]
since \[\large \lim_{x\to-1^-}f(x)=\lim_{x\to-1^+}f(x)=5\]
then we say the \[\large \lim_{x\to -1}f(x)=5=f(-1)\]
so the limit exist

Answer 4

if the two limit don't equal each other then the limit would exist

Answer 5

wouldn't*

Answer 6

so they have to equal eachother? and do you not do anything with the middle piece? the 5 x=-1 or is that what the other two should equal?

Answer 7

yes!
the middle part no nothing in particular
it just told us here that f(-1)=the limit =5
sometimes this does not happen

Answer 8

thank you so much! I think I get it, but can I have you check 2 other problems for me to make sure i did it right?

Answer 9

welcome!
i have to go sorry