Derive version 6.10 DfW file saved on 03 Jan 2008 -CI(z):=PROG(IF(z = 221e, RETURN 0), IF(z = -221e, RETURN e7c200b7e7c1), e7c3 + LN(z) + 222b((COS(z00b7t_) - 1)/t_, t_, 0, 1)) DER(u):=2202(u, x, 1) EI(x, m):=e7c3 + LN(x) + 2211(x^n_/(n_00b7n_!), n_, 1, m) EI1(z, m):=-e7c3 - LN(z) - 2211((-z)^n_/(n_00b7n_!), n_, 1, m) EN(n, z):=222b(e7c0^(- z00b7t_)/t_^n, t_, 1, 221e) EN_ASYMP(n, z, m):=e7c0^(-z)/z00b72211(PERM(n + l_ - 1, l_)/(-z)^l_, l_, 0, m) EVAL(u, a):=ITERATE(u, x, a, 1) F(x):=SIN(x^2) LI(x, m):=EI(LN(x), m) LINEA(u, a, b):=y = EVAL(u, a) + PENDSEC(u, a, b)00b7(x - a) PENDSEC(u, a, b):=(EVAL(u, a) - EVAL(u, b))/(a - b) PENDTAN(u, a):=EVAL(DER(u), a) SECANT(u, a, s):=[VECTOR(LINEA(u, a, b), b, a + 600b7s, a + s, -s)] SECANTES(u, a, s, n):=[VECTOR(LINEA(u, a, b), b, a + n00b7s, a + s, -s)] SI(z):=PROG(IF(z = 221e, RETURN e7c2/2), IF(z = -221e, RETURN - e7c2/2), 222b(SIN(z00b7t_)/t_, t_, 0, 1)) TANG(u, a):=y - EVAL(u, a) = PENDTAN(u, a)00b7(x - a) f(x):=e7c0^x g(X):=221a(X^2 + X) h(x):=x^4 + x^300b79 + x^200b727 + x00b727 l(x):=x^(2/3) m(x):=ABS(x)/(x^2 + 1) r(x):=COS(x)00b7e7c6(-221e, x, 0) + (1 - x)00b7e7c6(0, x, 221e) u(x):=200b7x00b7ATAN(200b7x) + LN(221a(1 + 400b7x^2)) v(x):=x00b7e^x hCross:=APPROX(1/2) vCross:=APPROX(41129032258064511/10000000000000000) y:=X00b7e7c0^X Precision:=Exact PrecisionDigits:=13 Notation:=Rational NotationDigits:=13 Branch:=Real Exponential:=Auto Logarithm:=Auto Trigonometry:=Auto Trigpower:=Auto Angle:=Radian CaseMode:=Insensitive VariableOrder:=[x,z] OutputBase:=Decimal InputBase:=Decimal InputMode:=Character DisplayFormat:=Normal TimesOperator:=Dot DisplaySteps:=false WCTextObj@{\rtf1\ansi\ansicpg1252\deff0\deflang3082{\fonttbl{\f0\fmodern\fprq1\fcharset0 Derive Unicode;}} \viewkind4\uc1\pard\f0\fs24 Pr\'e1ctica 2\'aa - Derivadas. Aplicaciones de las derivadas\par \par Diego Antonio Lucena Pumar\par } P{\rtf1\ansi\ansicpg1252\deff0\deflang3082{\fonttbl{\f0\fmodern\fprq1\fcharset0 Derive Unicode;}} \viewkind4\uc1\pard\f0\fs24 1.Derivada de una funci\'f3n en un punto\par \par Ejercicio 1\par } CExpnObj8NuevaF(x):=SIN(x^2)8Nueva"(F(1+h)-F(1))/h"8 Lim(#2,h)"LIM((F(1+h)-F(1))/h,h,0,0)"(Simp(#3)2*COS(1) 80 Aprox(#4) 1.0806046118@PNueva"(F(3+h)-F(3))/h"8`p Lim(#6,h)"LIM((F(3+h)-F(3))/h,h,0,0)"(Simp(#7)Mb?6*COS(9){\rtf1\ansi\ansicpg1252\deff0\deflang3082{\fonttbl{\f0\fmodern\fprq1\fcharset0 Derive Unicode;}} \viewkind4\uc1\pard\f0\fs24\par } 8 Aprox(Nueva)  -5.4667815718@Nueva #"(F(SQRT(pi)/2+h)-F(SQRT(pi)/2))/h"8 Lim(#10,h) ."LIM((F(SQRT(pi)/2+h)-F(SQRT(pi)/2))/h,h,0,0)" (PSimp(Lim(Nueva,h)) SQRT(2)*SQRT(pi)/2`8p Aprox(Nueva)  1.253314137{\rtf1\ansi\ansicpg1252\deff0\deflang3082{\fonttbl{\f0\fmodern\fprq1\fcharset0 Derive Unicode;}} \viewkind4\uc1\pard\f0\fs24 Ejercicio 2\par } 88Nuevag(x):=1+(x-2)^2*SIN(1/(x-2))8Nueva"(g(2+h)-g(2))/h"8 Lim(#15,h)"LIM((g(2+h)-g(2))/h,h,2,0)" 0P Simp(#16) 2*SIN(1/2)`8p Aprox(#17) 0.95885107728XNuevag(2) Aprox(#19)18Nueva"(g(2+h)-g(2))/h"8 Lim(#21,h)"LIM((g(2+h)-g(2))/h,h,0,0)" Aprox(#22)08 0Nueva"(g(-1+h)-g(-1))/h"8@P Lim(#24,h)"LIM((g(-1+h)-g(-1))/h,h,0,0)"`8p Aprox(#25) 1.018211234{\rtf1\ansi\ansicpg1252\deff0\deflang3082{\fonttbl{\f0\fmodern\fprq1\fcharset0 Derive Unicode;}} \viewkind4\uc1\pard\f0\fs24 Ejercicio 3\par } 8Nuevam(x):=ABS(x)/(x^2+1)8Nueva"(m(0+h)-m(0))/h"8  Lim(#28,h)"LIM((m(0+h)-m(0))/h,h,0,0)"0@ Aprox(#29)"+-"18P` Lim(#28,h)"LIM((m(0+h)-m(0))/h,h,0,-1)"p Aprox(#31) -18 Lim(#28,h)!"LIM((m(0+h)-m(0))/h,h,0,1)" Aprox(#33)"1{\rtf1\ansi\ansicpg1252\deff0\deflang3082{\fonttbl{\f0\fmodern\fprq1\fcharset0 Derive Unicode;}} \viewkind4\uc1\pard\f0\fs24 Ejercicio 4\par } 8Nueva#l(x):=x^(1/3*2)CPlotObjF  C2DPlotView CExplicitPlot@@U #xy??I$I$?Zk?11??BM-6(`,