Help with a limit function

[april]

The sales of a new product over a period of time are expected to follow the relationship

S(x)=25,000x^2/5x^2+5,000

where x is the amount of money spent on advertising.

Evaluate lim (x ->inf) S(x)= _________

Any help with this is much appreciated! Thanks!!

 

[daon]

To start, multiply top and bottom of the fraction by 1/x^2, OR try to remember the rule for a limit of a ratio of polynomials having equal dgree.

 

[april]

To start, multiply top and bottom of the fraction by 1/x^2, OR try to remember the rule for a limit of a ratio of polynomials having equal dgree.

Thank you Daon. Unfortunately I never received the rule and I don't know how to multiply by 1/x^2 :roll:

 

[o_O]

\(\displaystyle \frac{25000x^{2}}{5x^{2} + 5000} \cdot \frac{\frac{1}{x^{2}}}{\frac{1}{x^{2}}}\)

Really, when you multiply both top and bottom by 1/x², you're just multiplying by 1. But the idea is to use the fact that:
\(\displaystyle \lim_{x \to \infty} \frac{1}{x^{n}} = 0\) for \(\displaystyle n > 0\). (one over a really big number is pretty close to 0)

So continuing on with multiplying by "1",
\(\displaystyle \lim_{x \to \infty}\left(\frac{25000}{5 + \frac{5000}{x^{2}}\right)\)

Can you see what's happening?