MA1104 

An Introduction to Maple 11

Section 1

restart

2*5 + 3^5-7/6;

2*ln(x) + (3**x)*tan(x)/6;

4*x^5 - sin(x)*ln(x)*(x^6+10);

evalf(tan(Pi/4)*exp(1),6);



Section 2

x:='x';

f := x -> sqrt(1+10*x^4+20*x^6);

f(2);

f(f(2));



Section 3

with(plots):

plot(tan(x),x=-6..6);

plot(tan(x),x=-6..6,y=-10..10);




graph1:=plot(cos(x),x=-3..1):

graph2:=plot(sin(x),x=0..3):

graph3:=plot([[-2,1],[3,1.5]],x=2..4):

display({graph1,graph2,graph3});




Section 4

solve(x^2+3*x-4=0, x);

fsolve(x^5-x^3-1=0, x);

fsolve(tan(x)-x=0,x=3*Pi/2..5*Pi/2);

fsolve({x+y^2-1=0,cos(x)-y-2=0},{x,y},{x=-1..1,y=-2..2});

solve(x^2+x > 8*x, x);




Section 5

limit(sin(x)/x,x=0);

f:=x->x/sqrt(x^2+1):

limit(f(x),x=-infinity);

limit(f(x),x=a,right);




Section 6

diff(x^4,x);

f:=x->x^2 + x^3 + ln(x);

diff(f(x),x);

D(f)(x);

D(f)(1);

f:='f'; g:='g';

diff(f(x)*g(x),x);


Section 7

int(1/(3+x^2),x=1..infinity);

evalf(%);



Section 8

plot3d(9-x^2-y^2,x=-3..3,y=-3..3);

f:=(x,y)->4*x^2-y^2;

plot3d(f(x,y),x=-3..3,y=-3..3);




Section 9

with(plots):

a:=-2.7;

graph1 := plot(k(x),x=-3.5..2,thickness=3):

line1 := plot(k(a)+D(k)(a)*(x-a),x=-3.5..-2):

display({graph1,line1});