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find_root-solve

f:8*x^3-36*x^2+54*x-27;

solve(f,x);

find_root(f,x,0,2);

Calculate

find_root-log

find_root(log(x)-0.20...

Calculate

find_root-log

find_root((1/a)*(log(...

Calculate

find_root-sin

f(x) := sin(x) - x/2;

find_root (f, x, 0.1...

Calculate

find_root

find_root(x^2=2^x,x,-...

Calculate

find_root

find_root(x^2-4+0,x,0...

Calculate

find_root-tan

find_root(tan(x)-x-0....

Calculate

find_root-integrate

f(x):=x^3-3*x^2-4*x+3;

g(x):=x;

l(x):=f(x)-g(x);

Calculate

find_root-sin

f(x):=sin(x);

find_root(f,0,1);

Calculate

find_root-float-length-solve-sum

ref(r,m):=((1+r/m)^m-1);

find_root(ref(0.03923...

AIPV(A,r,t,m):=A*sum(...

Calculate

find_root

Run Example
(%i1)f1(x):=(x-3*%i)*(x+3*%i)*(x-%i)*(x+%i);
(%o1)          f1(x) := (x - 3 %i) (x + 3 %i) (x - %i) (x + %i)
(%i2) f1(x),expand;
                                 4       2
(%o2)                           x  + 10 x  + 9
(%i3) f2(x):=(x-3)*f1(x);
(%o3)                       f2(x) := (x - 3) f1(x)
(%i4) f2(x),expand;
                      5      4       3       2
(%o4)                x  - 3 x  + 10 x  - 30 x  + 9 x - 27
(%i5) f3(x):=(x-3)*(x+3)*(x-%i)*(x+%i);
(%o5)             f3(x) := (x - 3) (x + 3) (x - %i) (x + %i)
(%i6) f3(x),expand;
                                  4      2
(%o6)                            x  - 8 x  - 9
(%i7) f4(x):=(x-1)*f3(x);
(%o7)                       f4(x) := (x - 1) f3(x)
(%i8) f4(x),expand;
                         5    4      3      2
(%o8)                   x  - x  - 8 x  + 8 x  - 9 x + 9
(%i9) f5(x):=(x-5)*(x-2)*(x+1)*(x+3);
(%o9)              f5(x) := (x - 5) (x - 2) (x + 1) (x + 3)
(%i10) f5(x),expand;
                          4      3       2
(%o10)                   x  - 3 x  - 15 x  + 19 x + 30
(%i11) f6(x):=x*f5(x);
(%o11)                         f6(x) := x f5(x)
(%i12) f6(x),expand;
                        5      4       3       2
(%o12)                 x  - 3 x  - 15 x  + 19 x  + 30 x
(%i13) f7(x):=x! - 2^x;
                                              x
(%o13)                         f7(x) := x! - 2
(%i14) LOAD(CGAMMA);
(%o14)                           LOAD(CGAMMA)
(%i15) f8(x) := Gamma.logGamma( x + 1 ) - x * Log(2);
(%o15)            f8(x) := Gamma . logGamma(x + 1) - x Log(2)
(%i16)  solve(p4(x)=0,x);
(%o16)                            [p4(x) = 0]
(%i17) find_root(f8(x), x, 0.1, 5);
(%o17)    find_root(Gamma . logGamma(x + 1) - Log(2) x, x, 0.1, 5.0)
(%i18) Gamma.logGamma(5.0);
(%o18)                       Gamma . logGamma(5.0)
(%i19) 
Run Example
f(x):=x^3-3*x^2-4*x+3;
                                 3      2
(%o1)                   f(x) := x  - 3 x  + (- 4) x + 3
(%i2) g(x):=x;
(%o2)                              g(x) := x
(%i3) l(x):=f(x)-g(x);
(%o3)                         l(x) := f(x) - g(x)
(%i4) find_root(l(x),x,-1.6,-1.4);
(%o4)                         - 1.534070196722732
(%i5) h(x):=(1/2)*x^4-x^3+(3/2)*x^2+3*x;
                                1  4    3   3  2
(%o5)                   h(x) := - x  - x  + - x  + 3 x
                                2           2
(%i6) h(0.48)-h(-1.5);
(%o6)                            - 3.07969992
(%i7) 
Run Example
define(t(theta), 6/4 - 3/(4*tan(theta)) + 3/(2*sin(theta)));
                                    3              3         3
(%o1)            t(theta) := - ------------ + ------------ + -
                               4 tan(theta)   2 sin(theta)   2
(%i2) define(tp(theta), diff(t(theta), theta));
                                    2
                               3 sec (theta)   3 cos(theta)
(%o2)             tp(theta) := ------------- - -------------
                                    2               2
                               4 tan (theta)   2 sin (theta)
(%i3) plot2d(tp(theta),[theta, 0, %pi/2],[y, -2, 2]);
plotplot2d(tp(theta),[theta, 0, %pi/2],[y, -2, 2]);cv: find_root(tp(theta)=0, theta, 0.8, 1.2);
(%o4)                          1.047197551196598
(%i5) define(tpp(theta), diff(t(theta), theta, 2));
                         2               4
                    3 sec (theta)   3 sec (theta)        3
(%o5) tpp(theta) := ------------- - ------------- + ------------
                    2 tan(theta)         3          2 sin(theta)
                                    2 tan (theta)
                                                                       2
                                                                  3 cos (theta)
                                                                + -------------
                                                                      3
                                                                   sin (theta)
(%i6) tpp(cv);
(%o6)                          1.732050807568879
(%i7) tp(0.0000001);
(%o7)                      - 7.4999999999999469E+13
(%i8) tp(%pi/2 - 0.000001);
(%o8)                          0.74999850000075
(%i9) t(cv);
(%o9)                          2.799038105676658
(%i10) plot2d(t(theta),[theta, 0, %pi/2]);
plotplot2d(t(theta),[theta, 0, %pi/2]);
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