MAT 212 Lecture Notes - Lecture 26: Nintendo Ds And 3Ds Storage Devices
Document Summary
9. 2 calculus with parametric curves notes: sterling. Provide a generalization to each of the key terms listed in this section. Parametric equations are the following equations for an xy-plane"s curve: x = f (t) y = g (t) a t b. The chain rule occurs when you have both f and g are di erentiable, which means that (f g) (x) = f (g (x)), which can be written by the following formula: d dx. [f (g (x))] = f (g (x)) g (x) Also, if you use substitution and let both y = f (u) and u = g(x), then the following can be expressed in the same way: dy dt dy dx. Dx dt dt ) ( dy dt ) ( dx. The following gives you the curve"s, which is c, slope: y dy dx = d2y dx2 = = dy dx dt (cid:19) (cid:18) dy dt ) ( dx.
