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EV33

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## Homework Statement

P(x)=a0*x^(p)+a1*x^(p-1)+a2*x^(p-2)...

Q(x)=b0*x^(q)+b1*x^(q-1)+b2*x^(q-2)...

f(x)=lim (n[tex]\rightarrow[/tex][tex]\infty[/tex])P(n)/Q(n)

prove what f(x) is equal to for when p<q,q<p,p=q

Find the different values of f(x)

## Homework Equations

The only information that I know I can use is the definition of a limit, the squeeze principle,, 1/n converges as n goes to infinity, the limit of a^n where a is a fixed number, and that you can multiply, add, and divide limits.

## The Attempt at a Solution

Let

P(n)/Q(n)=(a0*n^(p)+a1*n^(p-1)+a2*n^(p-2)...)/(b0*n^(q)+b1*n^(q-1)+b2*n^(q-2)...)

I'll just start off by asking my first question. It is not legal to divide the top by n^p and the bottom by n^q correct? I would assume its not ok to do because the ratio between the two is not 1.

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