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
So the answer is b).
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).