Recent content by danerape

This isn't for homework. Here is my attempt at a proof. 1.Say we are given a function y=f(x) 2.Differentiate implicit w.r.t. y and we see... 1=(df/dx)(dx/dy) 3. Now we can solve for the derivative of our choice! Now, my question is... doesn't the result of 2(implicit...

the above is in regard to the link provided

how can y=f(x) define y implicitly? that seems explicit.

and vice-versa of course

How does one go about rigorously proving that (dy/dx)=1/(dx/dy)? Thanks

Also, any critique of the paper is certainly welcome, before I submit it I will have it reviewed to make sure all is well. Thanks Dane PS, pretty hard to understand for a mining engineering major, lol

Could this in some ways be analogous to thinking of a direction field? Even though we know y to be a function of x while graphing the direction field of y'=f(x,y), we still graph lineal elements, which seems analogous to graphing in the z direction. Does f being continuous in, or on the...

Ok, after going thru the proof, the only think that still eludes me is the region of definition given in the theorem itself. The rectangle where f and the partial of f with respect to y are known to be continuous. I am thinking of this three dimensionally, and I do not know if this is the...

Thanks, Dane

Any ideas at all?

I feel as if I have made the correct substitution, what am I missing? See Attachment. Thanks, Dane

I curiously never had a problem solving Seperable Equations in the Seperable Equations chapter of the Boyce/Diprima book. I am the kind of person who likes to do things the long way, and encountered a problem solving for an Integrating Factor(Linear ODE, NOT EXACT) the long proofy way. I tend...

This is a problem from the Boyce and Diprima Elementary DE book. I solved this equation and got the correct solution. However, the author notes that the solution is defined on the interval (-2,3) only. I have found it to be defined (-inf,-2)u(-2,3)u(3,inf), or EVERYWHERE BUT x=-2, x=3. Is...

Wow, third shift is really getting to me. Thanks a lot.

I know how to evaluate this type of limit, my problem is algebraically getting to the point of writing lim((n+1)^n/n^n)=lim(1+1/n)^n. How do I go from my ratio test to seeing the limit as equal to the latter limit? Thanks