Question

Can somebody please help me with finding limits. I have four hw questions and i just dont understand .

Answer 1

1. lim f(x), f(x)={4-x x<-1}
x--> -1 {5 x=-1}
{x+6 x>-1}

Answer 2

find the limit from right and left using the correct definitions , if were both equal then it exists , otherwise it doesn't exist

Answer 3

could you explain further?

Answer 4

@Ahmad1

Answer 5

\[\lim_{x \rightarrow -1^-}f(x)=\lim_{x \rightarrow -1^-}4-x=5\]
\[\lim_{x \rightarrow -1+}f(x) =\lim_{x \rightarrow -1+}6+x=5\] the limit from both sides equal to five then we say that: \[\lim_{x \rightarrow -1}f(x)=5\]
further more, the value of the limit equaled f(-1), this means that the not only the does exist, also the function is contious on R