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Řešení rovnice f(x)=0

Příklad 11:

>    x^2*sin(x)-10=0;

x^2*sin(x)-10 = 0

>    plot({x^2*sin(x)-10},x=-15..15,y=-5..5);

[Maple Plot]

>    plot({10/x^2,sin(x)},x=-15..15,y=-5..5);

[Maple Plot]

>    fsolve(x^2*sin(x)-10=0,x=-7..-5);

-6.001887026

>    fsolve(x^2*sin(x)-10=0,x=-5..-3);

-3.871845988

>    fsolve(x^2*sin(x)-10=0,x=6..7);

6.520602526

>    fsolve(x^2*sin(x)-10=0,x=9..10);

9.309126615

>    fsolve(x^2*sin(x)-10=0,x=12..13);

12.62910989

Příklad 12:

>    x*cos(x)-4=0;

x*cos(x)-4 = 0

>    plot({x*cos(x)-4},x=-15..15,y=-2..2);

[Maple Plot]

>    plot({4/x,cos(x)},x=-15..15,y=-2..2);

[Maple Plot]

>    fsolve(x*cos(x)-4=0,x=5..6);

5.522434103

>    fsolve(x*cos(x)-4=0,x=7..8);

7.271506864

>    fsolve(x*cos(x)-4=0,x=-9..-8);

-8.353327193

>    fsolve(x*cos(x)-4=0,x=-11..-10);

-10.60897682

Příklad 13:

>    3*ln(x)-x+4=0;

3*ln(x)-x+4 = 0

>    plot({3*ln(x)-x+4},x=-15..15,y=-10..10);

[Maple Plot]

>    plot({3*ln(x),x-4},x=-15..15,y=-10..10);

[Maple Plot]

>    fsolve(3*ln(x)-x+4=0,x=0..1);

.2903879955

>    fsolve(3*ln(x)-x+4=0,x=10..12);

11.26513864

Příklad 14:

>    sqrt(x-1)-sin(x)=0;

(x-1)^(1/2)-sin(x) = 0

>    plot({sqrt(x-1)-sin(x)},x=-3..3,y=-3..3);

[Maple Plot]

>    plot({sqrt(x-1),sin(x)},x=-3..3,y=-3..3);

[Maple Plot]

>    fsolve(sqrt(x-1)-sin(x)=0,x=1..2);

1.897194306

Příklad 15:

>    exp(-x)-sin(x)=0;

exp(-x)-sin(x) = 0

>    plot({exp(-x)-sin(x)},x=-5..5,y=-5..5);

[Maple Plot]

>    plot({exp(-x),sin(x)},x=-5..5,y=-5..5);

[Maple Plot]

>    fsolve(exp(-x)-sin(x)=0,x=0..1);

.5885327440

>    fsolve(exp(-x)-sin(x)=0,x=2..4);

3.096363932

Příklad 16:

>    3*sin(x)+sin(3*x)-1=0;

3*sin(x)+sin(3*x)-1 = 0

>    plot({3*sin(x)+sin(3*x)-1},x=-5..5,y=-3..3);

[Maple Plot]

>    plot({3*sin(x),1-sin(3*x)},x=-5..5,y=-3..3);

[Maple Plot]

>    fsolve(3*sin(x)+sin(3*x)-1=0,x=-4..-3);

-3.312359857

>    fsolve(3*sin(x)+sin(3*x)-1=0,x=0..1);

.1707672035

>    fsolve(3*sin(x)+sin(3*x)-1=0,x=2..4);

2.970825450

Příklad 17:

>    10*sin(x)-sqrt(x)=0;

10*sin(x)-x^(1/2) = 0

>    plot({10*sin(x)-sqrt(x)},x=-10..10,y=-10..10);

[Maple Plot]

>    plot({10*sin(x),sqrt(x)},x=-10..10,y=-10..10);

[Maple Plot]

>    fsolve(10*sin(x)-sqrt(x)=0,x=2..4);

2.968437138

>    fsolve(10*sin(x)-sqrt(x)=0,x=6..7);

6.541829422

>    fsolve(10*sin(x)-sqrt(x)=0,x=8..10);

9.118029220

Příklad 18:

>    2*sin(5*x)+cos(5*x)=0;

2*sin(5*x)+cos(5*x) = 0

>    plot({2*sin(5*x)+cos(5*x)},x=-2..2,y=-2..2);

[Maple Plot]

>    plot({2*sin(5*x),-cos(5*x)},x=-2..2,y=-2..2);

[Maple Plot]

>    fsolve(2*sin(5*x)+cos(5*x)=0,x=-2..0);

-1.349366583

>    fsolve(2*sin(5*x)+cos(5*x)=0,x=0..1);

.5355890089

>    fsolve(2*sin(5*x)+cos(5*x)=0,x=1..1.5);

1.163907540

Příklad 19:

>    sqrt(x-2)-3*cos(x)=0;

(x-2)^(1/2)-3*cos(x) = 0

>    plot({sqrt(x-2)-3*cos(x)},x=0..10,y=-5..5);

[Maple Plot]

>    plot({sqrt(x-2),3*cos(x)},x=0..10,y=-5..5);

[Maple Plot]

>    fsolve(sqrt(x-2)-3*cos(x)=0,x=5..6);

5.370986378

>    fsolve(sqrt(x-2)-3*cos(x)=0,x=6..8);

7.011614260

Příklad 20:

>    sqrt(x+1)+2*sin(x)=0;

(x+1)^(1/2)+2*sin(x) = 0

>    plot({sqrt(x+1)+2*sin(x)},x=-2..8,y=-2..2);

[Maple Plot]

>    plot({sqrt(x+1),-2*sin(x)},x=-2..8,y=-2..2);

[Maple Plot]

>    fsolve(sqrt(x+1)+2*sin(x)=0,x=-2..0);

-.3982956934

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