if f(x)={2-x, x<-1
x, -1<=x<1
(x-1)^2, x>=1}
find limit (f(x), x, -1-)
limit (f(x), x, -1+)
I have graphed the functions above but do not know how to find the limits, can someone please explain the steps needed?
Thanks!
No, because I don't even know how to start finding limits. I have seen them written this way, but I don't know what it means. I don't care if you solve my particular problem, but if you could just show me some kind of example I could follow, it would be very helpful!
$\displaystyle \lim_{x \to -1^-} \cdots$ means "the limit as x tends to -1 from the left of ..."
$\displaystyle \lim_{x \to -1^+} \cdots$ means "the limit as x tends to -1 from the right of ..."
so when it asks $\displaystyle \lim_{x \to -1^-}f(x)$, you say, okay, i am coming from the left of -1, that means, i want the function as it is defined for x < -1, because those are the values to the left of -1. now i look at my function and realize that for x < -1, the function is 2 - x
so i want $\displaystyle \lim_{x \to -1^-} (2 - x)$
this function is continuous, so you can just plug in -1 to find the limit.
$\displaystyle \lim_{x \to -1^-} (2 - x) = 2 - (-1) = 3$
a similar story holds true for the other one-sided limit