SOLUTION: Which limit does not exist? a. lim x-->3 2-x/x+1 b. lim x-->2 x^2-9/x-2 c. lim x-->1 (x^2-2x-5) d. lim x-->2 x^2-6x+8/x-2 e. lim x-->3 (x^2-3x-1)

Question 1180348: Which limit does not exist?
a. lim x-->3 2-x/x+1
b. lim x-->2 x^2-9/x-2
c. lim x-->1 (x^2-2x-5)
d. lim x-->2 x^2-6x+8/x-2
e. lim x-->3 (x^2-3x-1)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

All of the limits shown exist.

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,

lim x-->2 of (x+3)/(x-2)

does not exist because the expression is undefined at x=2.

On the other hand, this limit DOES exist:

lim x-->2 of ((x+3)(x-2))/(x-2)

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.

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.

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

x^2-9/x-2 =

where undoubtedly the intended expression is

(x^2-9)/(x-2) =

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.

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