True or False. Explain.
If lim f(x)=L
x → a
then
f(a)=L
2 answers
sure looks like it to me
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.
Evaluating the limit is not the same as evaluating the function!
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.
Evaluating the limit is not the same as evaluating the function!
1 answer