Pre meds--please help me with a calculus question

[Eyegirl2k7]

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In calculus, one of the conditions of continuity is that the limit as x approaches a of a function f(x) has to have the value f(a). But, why then, when f(x) =x^2 and x =1 does
f(1)=1^2=1
but lim (x-->a) x^2=2x=2(1)=2. In this case, the limit does not equal the value of f(a). And apparently, according to the textbook, the function is continuous through x=1!

Am I on crack?
I am very confused.

Insight appreciated.
Eyegirl.

 

[owen_osh]

lim (x-->a) for x^2 is a^2

Basically, the idea of lim (x-->a) for f(x) is identical to saying f(a), just like you said earlier. The only time when finding the limit involves any work is when

1) the limit, a, doesn't exist, such as lim-->infinity

2) the value of f(a) is not defined, such as when substituting a into f(x) makes the denominator zero