# Limits at infinity

• May 20th 2008, 09:54 PM
lemontea
Limits at infinity
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?
• May 20th 2008, 10:54 PM
Jen
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?

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

Consider for very very large values of x for example $\displaystyle x=10^{99}$ if you tried to put this into a calculator you would get something like $\displaystyle 2.5 \times 10^{-96}=.00000000000....25$ 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 $\displaystyle f(x)=\frac{x-1}{x^2-1}$, shown below. Notice as $\displaystyle x\to1$, f(x) appears to approach 1/2. But the graph is not actually defined at that point.

Attachment 6427