<PRE><B>Question 1180348</B>
&lt;br&gt;
All of the limits shown exist.&lt;br&gt;
The only thing that could make a limit not exist anywhere in the types of expressions shown in the answer choices is having a binomial factor in the denominator that is not also a factor of the numerator.  For example,&lt;br&gt;
lim x--&gt;2 of (x+3)/(x-2)&lt;br&gt;
does not exist because the expression is undefined at x=2.&lt;br&gt;
On the other hand, this limit DOES exist:&lt;br&gt;
lim x--&gt;2 of ((x+3)(x-2))/(x-2)&lt;br&gt;
The limit in that example exists, because the expression is identical to (x+3) everywhere except at x=2, so the limit is (x+3) evaluated at x=2, which is 5.&lt;br&gt;
None of the expressions in the answer choices have a factor in the form (x-a) in the denominator; so all of the limits shown exist.&lt;br&gt;
The problem with the question as you post it is that required parentheses are missing in most of the answer choices.  For example, the expression in answer choice b. is&lt;br&gt;
x^2-9/x-2 = {{{x^2-9/x-2}}}&lt;br&gt;
where undoubtedly the intended expression is&lt;br&gt;
(x^2-9)/(x-2) = {{{(x^2-9)/(x-2)}}}&lt;br&gt;
My discussion above should help you identify exactly one of the answer choices as being a limit that does not exist -- as long as you write the expressions with the correct use of parentheses.&lt;br&gt;
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