Question

Function f(x)=x+5 if x<1
f(x)=5 if x>1
1)lim x->-1 f(x)=?
2)lim x->1+ f(x)=?
3)limx->1 f(x)=?

Answer 1

ok so we have \[f(x)=\begin{cases}x+5&\text{if}~x<1\\5&\text{if}~x>1\end{cases}\]

Answer 2

right:)

Answer 3

for limit from the left we take x+5 \[\lim_{x\to1^-}(x+5)=1+5=6\]
for the limit from the right take 5 \[\lim_{x\to 1+}5=5\]

Answer 4

for the last question
i will tell you that \[\lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)=L\]
then \[\lim_{x\to a}f(x)=L\] so the limit exist
if the two sided limits are not equal then the limit at a does not exist

Answer 5

find out what you have to do