Quote:
What Locke had meant to post
Also
f(x)=
2-x if x < -1
x if -1 < x < 1
(x-1)^2 if x > 1
It says to sketch the graph ( which I've done) and use it to determine the values of a for which lim x->a f(x) exists. I'm not sure what exactly theyre asking for.
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You should use the [code] tag since your post didn't come out at all what you were expecting. Did you read over your post to ensure that it made sense?
Also, you can simply say <= for "
less than or equal to" and >= for "
greater than or equal to" and we would have understood out of context (although stating the context wouldn't have hurt, either). I really didn't understand what you meant with the underlines until I actually put underlines under them...
Anyway, they're probably asking for which points does a limit exist. I'm not sure how much of your
calculus vocabulary has developed at this point but I'll say that the
limit obviously exists for all points of the function for which it is
continuous. So, because the different sections of the function is composed of continuous expressions (the expressions are functions, themselves, that are continuous), the only concern now is the points where it may not be continuous--that is, the borders between the different expressions. So, the questions you must ask yourself are these two:
- Is the function continuous at x = -1 ?
- Is the function continuous at x = 1 ?
I'll leave the rest as an exercise for the reader. I mean, you are supposed to
learn this stuff, right?