# Exercici 06.8

kill(all)$

## Apartat a)

f(x):=(x^2 + 1)/(x+1);

m1=m1:limit(f(x)/x, x, minf);
b1=b1:limit(f(x)-m1*x, x, minf);

y1(x):=m1*x+b1;

wxplot2d([f(x), y1(x)], [x,-10,-1.5])$

m2=m2:limit(f(x)/x, x, inf);
b2=b2:limit(f(x)-m2*x, x, inf);

y2(x):=m2*x+b2;

wxplot2d([f(x),y2(x)], [x,0,10] )$

wxplot2d([f(x),y1(x)], [x,-10,10] , [y, -10, 10])$

## Apartat b)

kill(all)$

f(x):=(x^3 + 1)/(x^2 + 1);

m1=m1:limit(f(x)/x, x, minf);
b1=b1:limit(f(x)-m1*x, x, minf);

y1(x):=m1*x + b1;

wxplot2d([f(x), y1(x)], [x,-10, 0])$

m2=m2:limit(f(x)/x, x, inf);
b2=b2:limit(f(x)-m2*x, x, inf);

y2(x):=m2*x + b2;

wxplot2d([f(x),y1(x)], [x,-5, 5] )$

## Apartat c)

kill(all)$

f(x):=sqrt(x^2+x+1);

m1=m1:limit(f(x)/x, x, minf);
b1=b1:limit(f(x)-m1*x, x, minf);

y1(x):=m1*x + b1;

wxplot2d([f(x), y1(x)], [x,-10, 0])$

m2=m2:limit(f(x)/x, x, inf);
b2=b2:limit(f(x)-m2*x, x, inf);

y2(x):=m2*x + b2;

wxplot2d([f(x), y2(x)], [x,0, 10])$

wxplot2d([f(x),y1(x),y2(x)], [x,-5,5], [y,-1, 6])$

## Apartat d)

kill(all)$

f(x):=sqrt( (x^3) / (x-1) ) ;

m1=m1:limit(f(x)/x, x, minf);
b1=b1:limit(f(x)-m1*x, x, minf);

y1(x):=m1*x + b1;

wxplot2d([f(x), y1(x)], [x,-5, 0])$

m2=m2:limit(f(x)/x, x, inf);
b2=b2:limit(f(x)-m2*x, x, inf);

y2(x):=m2*x + b2;

wxplot2d([f(x), y2(x)], [x,1.2, 5])$

wxplot2d([f(x),y1(x),y2(x)], [x,-5,5], [y,-2, 15])$