Function f(x)=x+5 if x1 1)lim x--1 f(x)=? 2)lim x-1+ f(x)=? 3)limx-1 f(x)=?

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)=?

xapproachesinfinity · Answer

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

anonymous · Answer

right:)

xapproachesinfinity · Answer

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 $$\lim_{x\to 1+}5=5$$

xapproachesinfinity · Answer

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

xapproachesinfinity · Answer

find out what you have to do