Derive version 6.10 DfW file saved on 19 Dec 2007 ECENTER_OF_CURVATURE(y, x):=CENTER_OF_CURVATURE_AUX([x, y], 2202(y, x), 2202(y, x, 2)) CENTER_OF_CURVATURE_AUX(v, d1, d2):=v + [-d1, 1]00b7(1 + d1^2)/d2 CIRCLE_AUX(v0, r, 03b1):=[v021931 + r00b7COS(03b1), v021932 + r00b7SIN(03b1)] CURVATURE(y, x):=CURVATURE_AUX(2202(y, x), 2202(y, x, 2)) CURVATURE_AUX(d1, d2):=d2/(1 + d1^2)^(3/2) IMP_CENTER_OF_CURVATURE(u, x, y):=CENTER_OF_CURVATURE_AUX([x, y], IMP_DIF(u, x, y, 1), IMP_DIF(u, x, y, 2)) IMP_CURVATURE(u, x, y):=CURVATURE_AUX(IMP_DIF(u, x, y, 1), IMP_DIF(u, x, y, 2)) IMP_DIF(u, x, y, default1):=IMP_DIF_AUX(- 2202(u, x)/2202(u, y), x, y, default1) IMP_DIF_AUX(d1, x, y, n):=ITERATE(2202(dk, x) + d100b72202(dk, y), dk, d1, n - 1) IMP_OSCULATING_CIRCLE(u, x, y, x0, y0, 03b8):=CIRCLE_AUX(LIM(IMP_CENTER_OF_CURVATURE(u, x, y), [x, y], [x0, y0]), LIM(IMP_CURVATURE(u, x, y), [x, y], [x0, y0])^(-1), x, 03b8) IMP_PERPENDICULAR(u, x, y, x0, y0):=LIM(LINE_AUX(x_, y_, - LIM(IMP_DIF(u, x, y, 1), [x, y], [x_, y_])^(-1), x), [x_, y_], [x0, y0]) IMP_TANGENT(u, x, y, x0, y0):=LIM(LINE_AUX(x_, y_, LIM(IMP_DIF(u, x, y, 1), [x, y], [x_, y_]), x), [x_, y_], [x0, y0]) LINE_AUX(x0, y0, d1, x):=y0 + d100b7(x - x0) NORMAL_LINE(u, v, v0, t):=v0 + t00b7LIM(GRAD(u, v), v, v0) OSCULATING_CIRCLE(y, x, 03b8):=CIRCLE_AUX(CENTER_OF_CURVATURE(y, x), 1/CURVATURE(y, x), 03b8) PARA_CENTER_OF_CURVATURE(v, t):=CENTER_OF_CURVATURE_AUX(v, PARA_DIF(v, t, 1), PARA_DIF(v, t, 2)) PARA_CURVATURE(v, t):=CURVATURE_AUX(PARA_DIF(v, t, 1), PARA_DIF(v, t, 2)) PARA_DIF(v, t, default1):=ITERATE(2202(dk, t)/2202(v21931, t), dk, v21932, default1) PARA_OSCULATING_CIRCLE(v, t, t0, 03c6):=CIRCLE_AUX(LIM(PARA_CENTER_OF_CURVATURE(v, t), t, t0), 1/LIM(PARA_CURVATURE(v, t), t, t0), 03c6) PARA_PERPENDICULAR(v, t, t0, x):=LIM(LINE_AUX(LIM(v21931, t, t_), LIM(v21932, t, t_), - 1/LIM(PARA_DIF(v, t, 1), t, t_), x), t_, t0, 0) PARA_TANGENT(v, t, t0, x):=LIM(LINE_AUX(LIM(v21931, t, t_), LIM(v21932, t, t_), LIM(PARA_DIF(v, t, 1), t, t_), x), t_, t0, 0) PERPENDICULAR(y, x, x0):=LIM(LINE_AUX(x_, LIM(y, x, x_), - 1/LIM(2202(y, x), x, x_), x), x_, x0, 0) POLAR_CENTER_OF_CURVATURE(r, 03b8):=PARA_CENTER_OF_CURVATURE([r00b7COS(03b8), r00b7SIN(03b8)], 03b8) POLAR_CURVATURE(r, 03b8):=PARA_CURVATURE([r00b7COS(03b8), r00b7SIN(03b8)], 03b8) POLAR_DIF(r, 03b8, default1):=PARA_DIF([r00b7COS(03b8), r00b7SIN(03b8)], 03b8, default1) POLAR_OSCULATING_CIRCLE(r, 03b8, 03b80, 03c6):=PARA_OSCULATING_CIRCLE([r00b7COS(03b8), r00b7SIN(03b8)], 03b8, 03b80, 03c6) POLAR_PERPENDICULAR(r, 03b8, 03b80, x):=PARA_PERPENDICULAR([r00b7COS(03b8), r00b7SIN(03b8)], 03b8, 03b80, x) POLAR_TANGENT(r, 03b8, 03b80, x):=PARA_TANGENT([r00b7COS(03b8), r00b7SIN(03b8)], 03b8, 03b80, x) TANGENT(y, x, x0):=LIM(LINE_AUX(x_, LIM(y, x, x_), LIM(2202(y, x), x, x_), x), x_, x0, 0) TANGENT_PLANE(u, v, v0):=LIM(GRAD(u, v), v, v0) 22c5 (v - v0) eval(u, a):=ITERATE(u, x, a, 1) f(x, y):=200b7e7c0^x00b7COS(y) ptangente(u, a, b):=vnormal(u, a, b)00b7[x - a, y - b, z - valor(u, a, b)] = 0 u(x, y):=LN(x^2 + y^2) - ATAN(y/x) v(x, y):=x^3 - x^200b7y + x00b7y^2 - y^3 valor(u, a, b):=ITERATE(eval(u, a), y, b, 1) vnormal(u, a, b):=valor(GRAD(u - z), a, b) d1:= d2:= default1:=1 hCross:=APPROX(1) r:=- y/221a(4 - y^2) t0:= v0:= vCross:=APPROX(1) x0:= y0:= 03b1:= 03b8:= 03b80:= 03c6:= Precision:=Exact PrecisionDigits:=10 Notation:=Rational NotationDigits:=10 Branch:=Principal Exponential:=Auto Logarithm:=Auto Trigonometry:=Auto Trigpower:=Auto Angle:=Radian CaseMode:=Insensitive VariableOrder:=[x,y,z] OutputBase:=Decimal InputBase:=Decimal InputMode:=Character DisplayFormat:=Normal TimesOperator:=Dot DisplaySteps:=false CTextObj{\rtf1\ansi\ansicpg1252\deff0\deflang3082{\fonttbl{\f0\fmodern\fprq1\fcharset0 Derive Unicode;}} \viewkind4\uc1\pard\f0\fs24 Pr\'e1ctica 4\'aa - Funciones de varias variables\par \par Diego Antonio Lucena Pumar\par \par 1.Representaci\'f3n gr\'e1fica\par \par Ejercicio 1\par } CExpnObj8Nueva z=x^2+y^2CPlotObj~n C3DPlotViewC3DExplicitPlot@V @U <<xyZ s?@bL;?htN=?@@@@zxyz???xyzBM26(2