Asked by TayB
True or False. Explain.
If lim f(x)=L
x → a
then
f(a)=L
If lim f(x)=L
x → a
then
f(a)=L
Answers
Answered by
Damon
sure looks like it to me
Answered by
Steve
Not at all. Just because the limit exists, that does not mean the function at x=a has the value L. It might not even be defined at all.
recall your previous example, f(x)=(x^2+x-2)/(x^2-1), where the limit as x->1 was 1.5, but the function was not defined there.
There was a hole. In fact, the function might have been defined to be 10 there, so while the limit exists, the actual value of the function could be anything or undefined.
<u>Evaluating the limit is not the same as evaluating the function!</u>
recall your previous example, f(x)=(x^2+x-2)/(x^2-1), where the limit as x->1 was 1.5, but the function was not defined there.
There was a hole. In fact, the function might have been defined to be 10 there, so while the limit exists, the actual value of the function could be anything or undefined.
<u>Evaluating the limit is not the same as evaluating the function!</u>
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