Question

Use the given piecewise function to find...

Answer 1

f(x) = x^2+4 if x<1
3 if x=1
x+4 if x>1

Use the given piecewise function to find... \[\lim f(x) _{x \rightarrow1}\] if it exists and determine if this function is continuous or not when x=1

Answer 2

@johnweldon1993

Answer 3

And again, I know the answer is \[\lim _{x \rightarrow 1}f(x)=5\];not continuous.. but im just not sure how to find it

Answer 4

So think of it like this

As x approaches 1

how can it approach 1? well it can approach it from the left side of the graph....orrrr we can approach it from the right side of the graph

Answer 5

So...if we approach x from the left side of the graph...we are at values LESS than 1....so we need to use the first part of the piecewise function because x is less than 1 at this time

So if we plug in 1, we will get x^2 + 4, 1^2 + 4, 1 + 4 = 5

Great!

Answer 6

Now! if we approach from the right side, we are at values greater than 1...so we need to use that last part of the function because we are >1

so

x + 4 becomes 1 + 4 = 5 again

this is why we know the limit is 5 when we approach 1

Answer 7

HOWEVER!!!! when we are AT 1....we equal 3

HOW!?!?!?! lol, well this means the function is NOT CONTINUOUS! because how can we be approaching 5 from both sides...and then when we DO get to 1...we equal 3? its impossible that we are on a continuous line

Answer 8

Hope that makes sense?? if not let me know I can think of another way to put it probably ^_^

Answer 9

Sorry, I am reading through it a couple times.. I'm still not getting it :/