f(x) =  (2*x + 1)*3*sin((x + 4)*sqrt(2))/(x + 13) 
set title "O grafico de y = f(x) no intervalo [-10,10] " 
set terminal postscript portrait enhanced color
set output 'exer04_01.eps'
plot f(x),0
delta = 0.000001
df(x) = (f(x+delta)-f(x))/delta 

a = -8.0; rho = 1.0;
b = 10;
r(x) = f(a) + df(a)*(x-a)            
set xrange [a-rho:a+rho]
set yrange [-b:b]
set arrow from a,0 rto a,f(a) 
set output 'exer04_02.eps'
plot f(x), r(x),0
pause -2

a = a - f(a)/df(a)
rho = rho/2;
set output "exer04_03.eps" 
set arrow from a,0 rto a,f(a)
set xrange [a-rho:a+rho]
r(x) = f(a) + df(a)*(x-a) 
plot f(x), r(x),0
pause -2

a = a - f(a)/df(a)
rho = rho/2;
set xrange [a-rho:a+rho]
set output "exer04_04.eps" 
set arrow from a,0 rto a,f(a) 
set xrange [a-rho:a+rho]
r(x) = f(a) + df(a)*(x-a)
plot f(x), r(x),0
pause -2

a = a - f(a)/df(a)
rho = rho/2;
set xrange [a-0.5:a+0.5]
set output "exer04_05.eps" 
set arrow from a,0 rto a,f(a) 
r(x) = f(a) + df(a)*(x-a)
set xrange [a-rho:a+rho]
plot f(x), r(x),0
pause -2

a = a - f(a)/df(a)
rho = rho/2;
set xrange [a-0.5:a+0.5]
set output "exer04_06.eps" 
set arrow from a,0 rto a,f(a) 
r(x) = f(a) + df(a)*(x-a)
set xrange [a-rho:a+rho]
plot f(x), r(x),0
pause -2