# Multiple Choice General Limit Question

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• Sep 21st 2008, 08:19 PM
gearshifter
Multiple Choice General Limit Question
If lim x->2^- f(x) = lim x->2^+ = -1, but f(2) = 1, then lim x->2 f(x).

What is the best answer for this limit?

a. is -1.
b. does not exist.
c. is infinite.
d. is 1.
• Sep 21st 2008, 08:28 PM
o_O
$\displaystyle \lim_{x \to a} f(x)$ exists iff $\displaystyle \lim_{x \to a^+} f(x) = \lim_{x \to a^-} f(x)$ and is equal to their limit.

This has nothing to do with the value at $\displaystyle f(a)$.
• Sep 21st 2008, 08:31 PM
Chris L T521
Quote:

Originally Posted by gearshifter
If lim x->2^- f(x) = lim x->2^+ = -1, but f(2) = 1, then lim x->2 f(x).

What is the best answer for this limit?

a. is -1.
b. does not exist.
c. is infinite.
d. is 1.

If the left hand and the right hand limits are the same, regardless of the value of the function at that point, the limit is the value of the left and right hand limits.

Lets say that $\displaystyle \lim_{x\to{x_0^-}}f(x)=\lim_{x\to{x_0^+}}f(x)=c$.

If $\displaystyle f(x_0)=f;~f\neq c$, it doesn't have an affect on the value of the limit. Thus $\displaystyle \lim_{x\to{x_0}}f(x)=c$

Does this make sense?

With this, determine the correct answer.

--Chris