Find Limit of F(x) at x=1: 2x^2, 3, x+

[bard]

F(x)= 2x^2, x<1
3, X=1
X+, x>1

Find

lim(x-->1) f(X)

f(1)=

not exactly sure how to do this. would not f(1) be just 3, since it is defined as that in the function. I am not sure about how to take that limit.

Thanks

 

[LeonhardEuler]

When it comes to the limit of a function at x=a, the value of the function at a is irrelevant. In fact the function may not even be defined at "a", but the limit could still exist. So the fact that f(1)=3 is irrelevant to the problem. When looking for the limit, we must find a number that the function gets very close to as x approaches "a". It must get close to the same number when approaching from the left or right, or else the limit does not exist. In the case of this function, I think you might have made an error in typing it when you said that F(x) is equal to "X+" for x>1. But whatever it is, just see what number the function gets close to as x gets close to 1 from the right and the left. If they are the same number, then this is the limit; if not, then the limit does not exist.

 

[bard]

sorry that should be x+1

 

[bard]

ok so

lim(x->1+)=(1+1)=2
lim(x->1-)=(1+1)=2 so the limit exists, i don't understand how that helps in finding the overall limit of F(x) at 1.

 

[LeonhardEuler]

So the limit is 2. The limit is just the number the function approaches from both the left and the right.