Find each limit if it exists. f(x)= {1+|3+x| if x not equal to 3, 2 if x=3}

a)lim as x approaches 3^+ f(x)=?
b) lim as x approaches 3^- f(x)=?
c) lim as x approaches 3 f(x)=?

Question

Find each limit if it exists. f(x)= {1+|3+x| if x not equal to 3, 2 if x=3}

a)lim as x approaches 3^+ f(x)=?
b) lim as x approaches 3^- f(x)=?
c) lim as x approaches 3 f(x)=?

auctoratrox · Answer

c) 2. I cannot understand the rest

anonymous · Answer

me neither but its exactly as written

auctoratrox · Answer

a)7
b)7

auctoratrox · Answer

if and only if 3^- does not equal 3.

anonymous · Answer

how did you arrive at those answers?

myininaya · Answer

@Auctoratrox Giving just answers doesn't help and it is against the code of conduct.
Since x approaches 3 (we aren't concerned what happens at x=3; just around x=3)
Now from the right of 3 we have the function 1+|3+x|
And from the left of 3 we have the function 1+|3+x|
Since 1+|3+x| is continuous at x=3 just use direct sub for both sides
And if left limit=right limit=L then the actual limit=L

anonymous · Answer

I want to know what it 3^- and 3^+ mean

myininaya · Answer

3^- from left of 3
3^+ from right of 3

auctoratrox · Answer

3^- means the number very close to 3 from the left, like 2.999...
3^+ is the number very close to 3 from the right, like 3.000...01

anonymous · Answer

okay thanks