Learning Guide Learning Guide

228 • Chapter 6: Examples from Calculusr 2 cos(θ) sin(θ) (r 2 cos(θ) 2 − r 2 sin(θ) 2 )limr→0 r 2 cos(θ) 2 + r 2 sin(θ) 2> value( % );0Thus, you can extend f as a continuous function by defining it to bezero at (0, 0).> f(0,0) := 0;f(0, 0) := 0The above assignment places an entry in f’s remember table. Here isthe graph of f.> plot3d( f, -3..3, -3..3 );The partial derivative of f with respect to its first parameter, x, is> fx := D[1](f);fx := (x, y) → y (x2 − y 2 ) x 2 yx 2 + y 2 + 2x 2 + y 2 − 2 x2 y (x 2 − y 2 )(x 2 + y 2 ) 2This formula does not hold at (0, 0).> fx(0,0);Error, (in fx) numeric exception: division by zero