Limits at infinity

Quote:

Originally Posted by lemontea

1)The average cost/disc in dollars incurred by AA records in pressing x videodiscs is given by the average cost function

C(x)=2.2+2500/x

Evaluate lim x-->infinity C(x) and interpret your result

2) true or false, if false why?...If limx-->a (x) exists, then f is defined at x=a
I think this is true...what do you think?

$\lim_{x \to \infty} (2.2+\frac{2500}{x})=2.2$

Consider for very very large values of x for example $x=10^{99}$ if you tried to put this into a calculator you would get something like $2.5 \times 10^{-96}=.00000000000....25$ with 95 zeros between the decimal and 25 which is essentially zero, and as x goes to infinity this would get closer and closer to zero.

so all you would have left is 2.2

Consider the graph of $f(x)=\frac{x-1}{x^2-1}$ , shown below. Notice as $x\to1$ , f(x) appears to approach 1/2. But the graph is not actually defined at that point.

Attachment 6427