danielS

Related rates are fairly easy, just take the derivative with respect to time (usually), so you use the chain rule on anything that changes with time. Therefor an equation relating, say, length of a square to it's area, would be able to tell you how fast the area grows as the rate grows: da/dl * dl/dt or f'(g(x))g'(x) implicit differentiation just means differentiating both sides of the equation with respect to some variable and solving for the derivative. Maybe this helps, maybe not. I'll go on an example real quick, say the length of a square grows at 2 feet per second? so: dl/dt = 2 f/s but it's known that A = l^2 so take the derivative of both sides of this equation with respect to t dA/dt = 2l * dl/dt and dl/dt is 2 feet per second... so the area grows at 4l feet per second, which as you can see grows faster as l becomes larger (makes sense eh?). So when one side is 2 feet long, it is growing at 8 f^2 / s The most difficult part of this for most people is understanding the chain rule portion of the work. I hope that I helped!

in my calculus class, we learned lim x->0 of sin(x) / x is 1 and that lim x -> 0 of cos(x) + 1 / x is 0, however we don't tackle l'hoptal (sp)'s rule until second semester.

Hi, my name is Daniel. I am in first semester calculus, and the teacher is very disorganized and skips sections whenever he cares to. Earlier in the semester he skipped the section on epsilon/delta limit proofs. By reading the book, I was able to understand the idea of finding d as a function of e such that for any e > 0, there is a corresponding e that satisfies |f(x)-L| < e if 0 |x-a| < d and that this refers to the distances on the f and x axes... The problem is not with my understanding of epsilon delta proofs, so much as it is the techniques that the book uses to proove them. It only has a few examples, and the techniques seem very diverse and random, with very little methodology. He is not going to include anything he skips on tests, but I don't like not knowing what I'm paying to learn. Can anybody help?