%-- 6.10.10 15:54 --%
f = @(x) x^2-x-2;
x = puleni(f,1,4,1e-5)
f = @(x) sin(1/x);
puleni(f,0.1,1,1e-16)
ezplot(f)
ezplot('sin(1/x)')
clc
clear
c = faktorial(5)
c = faktorial_r(5)
c = faktorial_r(0)
c = faktorial(0)
c = faktorial_r(3)
a=je_prvocislo(7)
a=je_prvocislo1(7)
a=je_prvocislo1(3)
a=je_prvocislo1(7)
a=je_prvocislo1(70)
a=je_prvocislo1(2)
isprime(70)
clear
clc
doc symbolic
help symbolic
x=3
clc
syms x
x = sym('x')
y = sym('y')
d1 = sym('1/2+4/3')
M = sym([2 1; 3 -2])
M = [2 1; 3 -2]
sym x; y = cos(x^2)
v = sqrt(sym(2))
v2=sqrt(2)
clc
clear
sym x; p = 3*x^2 - 2*x + 6
1/2 + 1/3
format long
1/2 + 1/3
sym((1/2) + (1/3))
clear
syms x y
f = x^2 -2*x + 1
subs(f,1)
subs(f,y)
c1 = sym(1/5+3/4-1/6)
double(c1)
latex(f)
A = sym(hilb(2)) % Hilbertova matice řádu 2
latex(A)
f = x^3-6*x^2+11*x-6
pretty(f)
exp(c*log(sqrt(a+b)))
syms c
exp(c*log(sqrt(a+b)))
syms a b c
exp(c*log(sqrt(a+b)))
simplify(ans)
v=exp(c*log(sqrt(a+b)))
simplify(v)
simple(v)
clc
syms a b
a^2 - b^2
expand(ans)
factor(ans)
clear
clc
syms u
ezplot(cos(u))
syms x y
ezplot(x^2-y^6)
figure
ezplot(x^2-y^6)
ezplot(cos(u))
close
figure
close all
ezplot(cos(x),sin(x),[0 2*pi])
ezpolar(cos(x),sin(x),[0 2*pi])
ezpolar(cos(u))
clc
figure
syms u
ezplot(cos(u))
h=ezplot(cos(u))
get(h)
set(h,'color',[0 .3 0])
clear
clc
syms x
int(x^2+3*x-5,0,2)
syms x; f3 = int(x^2+3*x-5)
i=subs(f3,2)-subs(f3,0)
syms a x
f = sin(a^2*x);
diff(f)
diff(f,a)
diff(x^3+5*x^2-5*x,2);
diff(x^3+5*x^2-5*x,2)
clc
syms x
y = x^2+3*x-5;
dy = diff(y)
ezplot(y) % graf fce, modrá čára
hold on % zachovat staré grafy
h = ezplot(dy); set(h,'color',[1 0 0]) % graf derivace, červená čára
hold off
funtool
close all
clc
limit(sin(x)/x)
limit(sin(a)/a)
limit(sin(a)/x)
doc limit
clc
limit(1/x,x,0,'left')
limit(1/x,x,0,'right')
s1 = symsum(1/s^2,1,inf)
syms s
s1 = symsum(1/s^2,1,inf)
s2=symsum(s^2,0,10)
s_obec=symsum(s^2)
subs(s_obec,11)
clc
dsolve('Dx = -a*x')
dsolve('(Dy)^2 + y^2 = 1','s')
dsolve('Dy = a*y', 'y(0) = b')
z = dsolve('Dx = y', 'Dy = -x')
z.y
z.x
clc
syms a b c x
solve('a*x^2+b*x+c')
solve('a*x^2+b*x+c','b')
S = solve('x + y = 1', 'x - 11*y = 5')
S.x
S.y
clc
syms a u v
A = solve('a*u^2 + v^2', 'u - v = 1', 'a^2 - 5*a + 6')
Aa = A.a, Au = A.u, Av = A.v
double(subs([a*u^2+v^2, u-v-1, a^2-5*a+6], {a,u,v}, {Aa(3),Au(3),Av(3)}))
clc
clear
%uloha 41
syms n
limit((n^2+5*n+1)/(n^3-3),inf)
limit(sqrt(n^3+2*n-1)/(n+2),inf)
limit(symsum(n^2,1,n)/(2*n^3+n^2-1,inf))
limit(symsum(n^2,1,n)/(2*n^3+n^2-1),inf)
%uloha 42
clear
syms x a b
limit((sin(x)/sin(a))^(1/(x-a)),x,a)
limit(atan(1/1-x),x,1,'right')
limit(atan(1/(1-x)),x,1,'right')
limit(atan(1/(1-x)),1,'right')
limit(atan(1/(1-x))1,'right')
limit(atan(1/(1-x)),x,1,'right')
clc
clear
%uloha 43
syms x
F1=int(1/(1+x^2))
diff(F1)
F3=int(x^2*log(x))
diff(F3)
pretty(ans)
clc
%uloha 44
d1=diff(cos(3*x^2+2*x+1)^3
d1=diff(cos(3*x^2+2*x+1)^3)
pretty(d1)
d1=diff(cos(3*x^2+2*x+1)^3,2)
d1=diff(cos(3*x^2+2*x+1)^3,3)
pretty(d1)
clc
%uloha 45
symsum((-1)^{n+1)*(x-1)^n/n,n,1,inf)
symsum((-1)^(n+1)*(x-1)^n/n,n,1,inf)
syms n
symsum((-1)^(n+1)*(x-1)^n/n,n,1,inf)
clear
clc
%uloha 46
f= dsolve('D2y+2*Dy+2*y=0')
syms x
y=exp(-y)*sin(x)
syms y
y=exp(-y)*sin(x)
diff(y,2)+2*diff(y)+2*y
y=exp(-x)*sin(x)
diff(y,2)+2*diff(y)+2*y
clc
clear
uloha49
clear
clc
uloha50
clear
clc
asteroida(1)
asteroida(2)
asteroida(10)
close
asteroida(-10)
asteroida(20)
cykloida(2,2)
cykloida(2,2,10*pi)
spirala_archim(2)
spirala_archim(20)
figure
spirala_archim(2)
clear
clc
primka(1,-2,0,1,1,2)
clc
primka(1,-2,0,1,1,2)