Recent content by fireychariot

I mean y = q/p sorry. What's confusing is the fact that it is variables as the constants instead of numbers so any more hints would be grateful.

-py+q=0 so do I say y = p/q how do I find the x coordinate from that? Is that when x =0 or do I substitute it into my second equation?

Homework Statement \dot{x} = -pxy + qx, \dot{y} = rxy - sy where p,q,r and s are positive constants (p does not equal r) Question is : Determine all the equilibrium points for the system of differential equations given above, expressing your answers in terms of p,q,r and s The...

Which method did you end up using though?

rohan03 how did you solve the problem you had here? I too am struggling with this.

All I have written then is this xn → 0 \Rightarrow 2xn+xn+3 → 3 where xn < 0 and xn→ 0 \Rightarrow \frac{3}{x+1} → 3 where xn≥0 This holds by the combination rules for sequences therefore f is continuous at 0. Is this all I have to write as it doesn't seem to be enough??

Homework Statement f(x) = {2x2 + x +3, x < 0 \frac{3}{x + 1} x ≥ 0 The 2 should be wrapped as 1 with a { but do not know how to do that. Homework Equations The Attempt at a Solution I was wondering if the squeeze rule would be...

Yes that's correct many thanks

What would the coefficients of n-1 and n-2 be then?

\frac{n!}{0!(n-0)!}1^{n} + \frac{n!}{(n!)(n-n)!}n^{n} + \frac{n!}{(n-1)!(n-(n-1))}n^{n-1}+\frac{n!}{(n-2)!(n-(n-2))}n^{n-2} + \cdots = 1 + n^{n} + and this is where I get stuck Am I on the right path by the way in solving the orginal problem?

thank you for your help so far. I want to see if i have expanded this right then. Definetly need more practice on this. (1+n)^n = 1^n + 1^n + n^n-1 + 1/2n^n-2 + \cdots

so say i was doing k = n-1 n(n-1)/n(n-1)(0)! = n(n-1)/0! = n(n-1)? have I don't that correct??

Thanks for that. I'm having a blonde moment though when working out the coefficients. I know you use n!/k!(n-k)! However I am little confused when I input for say k = n-1 I get n!/(n-1)!(n-n-1)! How do I expand on this? Many thanks.

what do you mean last 3 terms? if its infinite it wouldn't have any last term?