can anyone help me with a math 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.

 

[TAL]

Just pass the course and never think about calculus again! (I have no idea about your question.)

 

[rose13]

I'll try to assist, but I need to know what the symbol between the x and 2 is. 🙂

 

[Eyegirl2k7]

The symbol between x and 2 means "squared"

Thanks,
Eyegirl (still fumbling with the calculus)

 

[rpames]

I actually remember asking the same question last semester. The funny thing is, I don't remember the answer. I'm going to email a freind and see what she says. I'll be back.

 

[mpp]

The lim(x->1)f(x)=x^2 = 1

You do not have to take the derivative of x^2 as you did in your example. To find the value of a function as the variable approaches some value, just substitute that value into the function. You are confusing limits with the definition of a derivative.

The definition of a derivative is

f'(x) = lim(dx->a) (f(x+dx)-f(x))/dx

This has nothing to do with your original question regarding the limit of x^2 as x approaches 1.

Hope this is clear.