Academic License

x=linspace(0,2,100);
plot(x,sin(x))

x=linspace(0,3,100);
plot(x,sin(x))
hold on
plot(x,x/2)
fsolve(@(x)(sin(x)=x/2),1);
 fsolve(@(x)(sin(x)=x/2),1);
                   |
{Error: The expression to the left of the equals sign is not a valid target for an assignment.
} 
fsolve(@(x)(sin(x)-x/2),1);

<a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'eqn_solved','CSHelpWindow');">Equation solved</a>.

fsolve completed because the vector of function values is near zero
as measured by the default value of the <a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'fcn_tolerance_fsolve','CSHelpWindow');">function tolerance</a>, and
the <a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'appears_regular','CSHelpWindow');">problem appears regular</a> as measured by the gradient.

<<a href = "matlab: createExitMsg('trustnleqn',1.000000e+00,true,true,'fsolve',0.000000e+00,'default',1.000000e-06,0.000000e+00,'default',1.000000e-03,0.000000e+00,'default',1.000000e-03);">stopping criteria details</a>>

x1=fsolve(@(x)(sin(x)-x/2),1);

<a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'eqn_solved','CSHelpWindow');">Equation solved</a>.

fsolve completed because the vector of function values is near zero
as measured by the default value of the <a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'fcn_tolerance_fsolve','CSHelpWindow');">function tolerance</a>, and
the <a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'appears_regular','CSHelpWindow');">problem appears regular</a> as measured by the gradient.

<<a href = "matlab: createExitMsg('trustnleqn',1.000000e+00,true,true,'fsolve',0.000000e+00,'default',1.000000e-06,0.000000e+00,'default',1.000000e-03,0.000000e+00,'default',1.000000e-03);">stopping criteria details</a>>

x1

x1 =

     0

fsolve(@(x)(sin(x)-x/2),3)

<a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'eqn_solved','CSHelpWindow');">Equation solved</a>.

fsolve completed because the vector of function values is near zero
as measured by the default value of the <a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'fcn_tolerance_fsolve','CSHelpWindow');">function tolerance</a>, and
the <a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'appears_regular','CSHelpWindow');">problem appears regular</a> as measured by the gradient.

<<a href = "matlab: createExitMsg('trustnleqn',1.000000e+00,true,true,'fsolve',9.732645e-09,'default',1.000000e-06,1.412115e-16,'default',1.000000e-03,1.412115e-16,'default',1.000000e-03);">stopping criteria details</a>>


ans =

    1.8955

createExitMsg('trustnleqn',1.000000e+00,true,true,'fsolve',9.732645e-09,'default',1.000000e-06,1.412115e-16,'default',1.000000e-03,1.412115e-16,'default',1.000000e-03);

Equation solved. The sum of squared function values, r = 1.412115e-16, is less than
sqrt(<a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'tolfun_fsolve','CSHelpWindow');">options.TolFun</a>) = 1.000000e-03. The relative norm of the gradient of r, 9.732645e-09,
is less than options.TolFun = 1.000000e-06.

Optimization Metric                                             Options
relative norm(grad r) =   9.73e-09                     TolFun =   1e-06 (default)
r =   1.41e-16                                  sqrt(TolFun) =  1.0e-03 (default)

X=3

X =

     3

X= 2* sin(X)

X =

    0.2822

X= 2* sin(X)

X =

    0.5570

X= 2* sin(X)

X =

    1.0573

X= 2* sin(X)

X =

    1.7421

X= 2* sin(X)

X =

    1.9707

X= 2* sin(X)

X =

    1.8422

X= 2* sin(X)

X =

    1.9268

X= 2* sin(X)

X =

    1.8746

X= 2* sin(X)

X =

    1.9084

X= 2* sin(X)

X =

    1.8871

X= 2* sin(X)

X =

    1.9008

X= 2* sin(X)

X =

    1.8921

X= 2* sin(X)

X =

    1.8977

X= 2* sin(X)

X =

    1.8941

X= 2* sin(X)

X =

    1.8964

X= 2* sin(X)

X =

    1.8949

X= 2* sin(X)

X =

    1.8959

X= 2* sin(X)

X =

    1.8953

X= 2* sin(X)

X =

    1.8956

X= 2* sin(X)

X =

    1.8954

X= 2* sin(X)

X =

    1.8956

X= 2* sin(X)

X =

    1.8955

X= 2* sin(X)

X =

    1.8955

X= 2* sin(X)

X =

    1.8955

X= 2* sin(X)

X =

    1.8955









x=linspace(0,3,100);
plot(x)
hold off
plot(sin(x))
plot(x,sin(x))
hold on
plot(x,x/2)
plot(x,sin(x)-x/2)
fsolve(@(x)(sin(x)-x/2),3)

<a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'eqn_solved','CSHelpWindow');">Equation solved</a>.

fsolve completed because the vector of function values is near zero
as measured by the default value of the <a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'fcn_tolerance_fsolve','CSHelpWindow');">function tolerance</a>, and
the <a href = "matlab: helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'appears_regular','CSHelpWindow');">problem appears regular</a> as measured by the gradient.

<<a href = "matlab: createExitMsg('trustnleqn',1.000000e+00,true,true,'fsolve',9.732645e-09,'default',1.000000e-06,1.412115e-16,'default',1.000000e-03,1.412115e-16,'default',1.000000e-03);">stopping criteria details</a>>


ans =

    1.8955

helpview([docroot '/toolbox/optim/msg_csh/optim_msg_csh.map'],'eqn_solved','CSHelpWindow');
sin(ans)

ans =

    0.9477

2*ans

ans =

    1.8955

X=2

X =

     2

X= 2* sin(X)

X =

    1.8186

X= 2* sin(X)

X =

    1.9389

X= 2* sin(X)

X =

    1.8660

X= 2* sin(X)

X =

    1.9135

X= 2* sin(X)

X =

    1.8837

X= 2* sin(X)

X =

    1.9029

X= 2* sin(X)

X =

    1.8907

X= 2* sin(X)

X =

    1.8985

X= 2* sin(X)

X =

    1.8936

X= 2* sin(X)

X =

    1.8967

X= 2* sin(X)

X =

    1.8947

X= 2* sin(X)

X =

    1.8960

X= 2* sin(X)

X =

    1.8952

X= 2* sin(X)

X =

    1.8957

X= 2* sin(X)

X =

    1.8954

X= 2* sin(X)

X =

    1.8956

X= 2* sin(X)

X =

    1.8954

X= 2* sin(X)

X =

    1.8955

X= 2* sin(X)

X =

    1.8955

X= 2* sin(X)

X =

    1.8955

X= 2* sin(X)

X =

    1.8955

X= 2* sin(X)

X =

    1.8955

X=  sin(X)

X =

    0.9477

X=  sin(X)

X =

    0.8121


X=  sin(X)

X =

    0.7257

X=  sin(X)

X =

    0.6637

X=  sin(X)

X =

    0.6160

X=  sin(X)

X =

    0.5778

X=  sin(X)

X =

    0.5462

X=  sin(X)

X =

    0.5194

X=  sin(X)

X =

    0.4964

X=  sin(X)

X =

    0.4762

X=  sin(X)

X =

    0.4584

X=  sin(X)

X =

    0.4426

X=  sin(X)

X =

    0.4283

X=  sin(X)

X =

    0.4153

X=  sin(X)

X =

    0.4034

X=  sin(X)

X =

    0.3926

X=  sin(X)

X =

    0.3826

X=  sin(X)

X =

    0.3733

X=  sin(X)

X =

    0.3647

X=  sin(X)

X =

    0.3567

X=  sin(X)

X =

    0.3492

X=  sin(X)

X =

    0.3421

X=  sin(X)

X =

    0.3355

X=  sin(X)

X =

    0.3292

X=  sin(X)

X =

    0.3233

X=  sin(X)

X =

    0.3177

X=  sin(X)

X =

    0.3124

X=  sin(X)

X =

    0.3073

X=  sin(X)

X =

    0.3025

X=  sin(X)

X =

    0.2979

X=  sin(X)

X =

    0.2935

X=  sin(X)

X =

    0.2893

X=  sin(X)

X =

    0.2853

X=  sin(X)

X =

    0.2815

X=  sin(X)

X =

    0.2778

X=  sin(X)

X =

    0.2742

X=  sin(X)

X =

    0.2708

X=  sin(X)

X =

    0.2675

X=  sin(X)

X =

    0.2643

X=  sin(X)

X =

    0.2612

X=  sin(X)

X =

    0.2583

X=  sin(X)

X =

    0.2554

X=  sin(X)

X =

    0.2526

X=  sin(X)

X =

    0.2500

X=  sin(X)

X =

    0.2474

X=  sin(X)

X =

    0.2449

X=  sin(X)

X =

    0.2424

X=  sin(X)

X =

    0.2400

X=  sin(X)

X =

    0.2377

X=  sin(X)

X =

    0.2355

X=  sin(X)

X =

    0.2333

X=  sin(X)

X =

    0.2312

X=  sin(X)

X =

    0.2292

X=  sin(X)

X =

    0.2272

X=  sin(X)

X =

    0.2252

X=  sin(X)

X =

    0.2233

X=  sin(X)

X =

    0.2215

X=  sin(X)

X =

    0.2197

X=  sin(X)

X =

    0.2179

X=  sin(X)

X =

    0.2162

X=  sin(X)

X =

    0.2145

X=  sin(X)

X =

    0.2129

X=  sin(X)

X =

    0.2113

X=  sin(X)

X =

    0.2097

X=  sin(X)

X =

    0.2082

X=  sin(X)

X =

    0.2067

X=  sin(X)

X =

    0.2052

X=  sin(X)

X =

    0.2038

X=  sin(X)

X =

    0.2023

X=  sin(X)

X =

    0.2010

X=0.6

X =

    0.6000

X=  exp(X)/3

X =

    0.6074

X=  exp(X)/3

X =

    0.6119

X=  exp(X)/3

X =

    0.6146

X=  exp(X)/3

X =

    0.6163

X=  exp(X)/3

X =

    0.6174

X=  exp(X)/3

X =

    0.6180

X=  exp(X)/3

X =

    0.6184

X=  exp(X)/3

X =

    0.6187

X=  exp(X)/3

X =

    0.6188

X=  exp(X)/3

X =

    0.6189

X=  exp(X)/3

X =

    0.6190

X=  exp(X)/3

X =

    0.6190

X=  exp(X)/3

X =

    0.6190

X=  exp(X)/3

X =

    0.6190

X=  exp(X)/3

X =

    0.6190

format long
X

X =

   0.619047309788707

X

X =

   0.619047309788707

X=  exp(X)/3

X =

   0.619052634209471

X=  exp(X)/3

X =

   0.619055930314946

X=  exp(X)/3

X =

   0.619057970791950

X=  exp(X)/3

X =

   0.619059233966792

X=  exp(X)/3

X =

   0.619060015947336

X=  exp(X)/3

X =

   0.619060500040414

X=  exp(X)/3

X =

   0.619060799723389

X=  exp(X)/3

X =

   0.619060985245399

X=  exp(X)/3

X =

   0.619061100094848

X=  exp(X)/3

X =

   0.619061171193678

X=  exp(X)/3

X =

   0.619061215208205

X=  exp(X)/3

X =

   0.619061242455892

X=  exp(X)/3

X =

   0.619061259323879

X=  exp(X)/3

X =

   0.619061269766196

X=  exp(X)/3

X =

   0.619061276230631

X=  exp(X)/3

X =

   0.619061280232512

X=  exp(X)/3

X =

   0.619061282709921

X=  exp(X)/3

X =

   0.619061284243590

X=  exp(X)/3

X =

   0.619061285193024