use the following graph to answer he three questions
(1) which of the statements is valid
(a) lim x->1 f(x)=2
(b)lim x->1 f(x)=0
(c) lim x->1 f(x) doesnot exist
(2) what is lim x->2+ f(x)?
(a)0 (b) 2 (c) limit does not exist
(3) which ,If any, of these limits exists
(a) lim x->2+f(x)
(b) lim x-> 2- f(x)
(c) lim x-> -3 f(x)
d) none of the above
We are looking at what is happening to f(x) as x approaches 2 from the "+" side, or from the right. Since this is a "one-sided" limit, we don't care about what happens from the other side. So what does f(x) approach as we get close to x = 2 from the right? f(x) approaches the value 2. In this case we even have that f(2) = 2.
So the answer is b).
-Dan
Well, we'd better hope that the limit in a) exists because that was problem 2! So yes, a) is an answer.
Looking at the limit of f(x) as x approaches 2 from the "-", or left, side we see that the function value "blows down" (as opposed to blows up) to negative infinity. So this limit does not exist.
There is nothing strange going on at x = -3. It is easy to see that the limit exists on both sides of x = -3 and that f(x) approaches the same value in each case. (f(-3) is about 2 or so). So this limit also exists.
So the answer(s) is a) and c).
-Dan