### Related

##### find_root-integrate-plot2d-ratsimp-sqrt-subst

xs: sqrt(g^2*(1-g^2/(...

i1: integrate(-r+sqrt...

e1: ratsimp(2 * (subs...

Calculate

##### find_root-numer-solve

find_root(30=c*(28000...

helligkeit(messwert):...

solve(helligkeit(x)=3...

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##### find_root-float-plot2d-sin

plot2d([5*sin(x),4*x]...

ans:find_root(5*sin(x...

float(ans*180/%pi);

Calculate

##### find_root-fpprintprec

fpprintprec:3;

f(x):=(((-15*x^4+6*x-...

find_root(f(x),x,0,1);

Calculate

##### find_root

find_root(-4*x*x*x*x ...

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##### find_root

f:x^2-6*x-7;

find_root(f,x,-1,1);

find_root(f,x,1,10);

Calculate

##### find_root-inf

find_root(10=10*log10...

find_root(10=x,x, 0, ...

2 +2;

Calculate

##### find_root-sin

find_root(3*sin(x)=x,...

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##### find_root-sin

find_root(1-x/sin(x)=...

Calculate

##### find_root-floor-makelist-plot2d-transpose

"*"/* Ein Unternehmen...

"*"/* Lösung (n sind ...

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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
(%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
```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]);
plotcv: 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]);
plot```
Run Example
```intervals(items):=block([result],  result: if (emptyp(items)) then [] else           if(listp(items)) then          if(emptyp(rest(items))) then [] else          cons(cons(first(items),  [second(items)]),          intervals(rest(items))));
(%o1) intervals(items) := block([result],
result : if emptyp(items) then [] else (if listp(items)
then (if emptyp(rest(items)) then [] else cons(cons(first(items),
[second(items)]), intervals(rest(items))))))
(%i2) intervals(makelist(n, n, 1, 10));
(%o2) [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]
(%i3) intervals(makelist(n, n, 1, 11));
(%o3) [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9],
[9, 10], [10, 11]]
(%i4) ans:errcatch(find_root(sin(x), x, 2, 3));

find_root: function has same sign at endpoints: f(2.0) = 0.90929742682568,
f(3.0) = 0.14112000805987
(%o4)                                 []
(%i5) ans;
(%o5)                                 []
(%i6) seq(start,stop,stepping,[shift]) := block([                                            n, y:[],                                             shift: (if (not(emptyp(shift)))                                                         then float(first(shift))                                                            else (0.0))                                            ],            (n:floor((float(stop-start)/float(stepping)))),            (if (start <
stop)            then            (y:flatten(append([y],                                         makelist(float(start+shift+(stepping*(i-start))),                                         i, start, n+start))))            else            (y:flatten(append([y],                                         makelist(-(float(stop-shift-(stepping*(i-stop)))),                                         i, -(n+stop), stop)))))            (if (n>
1.0)                then return(y)                else return([])));
(%o6) seq(start, stop, stepping, [shift]) :=
block([n, y : [], shift : if not emptyp(shift) then float(first(shift))
float(stop - start)
else 0.0], n : floor(-------------------),
float(stepping)
if start < stop then y : flatten(append([y],
makelist(float(start + shift + stepping (i - start)), i, start, n + start)))
else y : flatten(append([y], makelist(- float(stop - shift
- stepping (i - stop)), i, - (n + stop), stop)))(if n > 1.0 then return(y)
else return([])))
(%i7) intervals(seq(0,7,1));
(%o7) [[0.0, 1.0], [1.0, 2.0], [2.0, 3.0], [3.0, 4.0], [4.0, 5.0], [5.0, 6.0],
[6.0, 7.0]]
(%i8) ans:[];
(%o8)                                 []
(%i9) %pi;
(%o9)                                 %pi
(%i10) %pi, numer;
(%o10)                         3.141592653589793
(%i11) 2*3.14159/%pi;
6.28318
(%o11)                              -------
%pi
(%i12) block([ans:[]], errormsg:false, for i in intervals(seq(0, 7, 1)) do ans:(append(ans, errcatch(find_root(sin(x), x, first(i), second(i))))), errormsg:true, return(ans));
(%o12)            [0.0, 3.141592653589793, 6.283185307179586]
(%i13) ```

### Related Help

Help for Find_root