Question

Find the indicated limit, if it exists.
HOW do I do this?!
Lim x-->5 f(x),f(x){5-x x<5
{8 x=5
{x+3 x>5
0

8

3

The limit does not exist

Answer 1

@amistre64 ?

Answer 2

it looks like you are given a piecewise function

Answer 3

the limit will only exist of 5-x = x+3, when x=5

otherwise the limit for the left and right of 5 do not match up

Answer 4

be sure that the question is not asking for a one-sided limit like:\[x\to 5^+\]

Answer 5

if we were to graph these it would look something like this:

Answer 6

notice:

if we come into x=5 from the left we approach 0
if we come into x=5 from the right we approach 8

since 8 does not equal 0, the limit of the function does not exist ....

Answer 7

I am plugging in 5 for X in each one and adding/subtracting the total to get my answer, is that right? and what do I do for the 8 x=5?

Answer 8

the limit of a function has no bearing on the value of the function at the limit point ....

the limit of a function only cares if the value from the left and the right are equal

Answer 9

we see that the value at x=5 is 8 ... the limit doesnt care what this value is ...

the value from the left as x approaches 5 is defined by (x-5)
the value from the right as x approaches 5 is defined by (x+3)

x-5 has no bad calculations in it so itll just be: 5-5 = 0
x+3 has no bad calculations in it so itll just be: 5+3 = 8

since 8 is not equal to 0, the limit does not exist

Answer 10

So i'm not plugging in 5 for x?

Answer 11

your not caring that the function defines f(5) = 8. otherwise, yes.

you are comparing the definition of the function from left and right as the values of x approach 5.

Answer 12

if the values are not the same, then there is no limit