恩，平方级收敛.
很久没写这些基础算法了，练习一下
f:=x+Sinh-2;
FindRoot==0,{x,0},WorkingPrecision->50]
{x->0.93000903471256505280413348817639994538119999150908}
NestList[#-f[#]/f'[#]&,2`50,10]
2.0000000000000000000000000000000000000000000000000
1.2384058440442351118805417173952064095872314027421
0.953198930036790515919472881710464898304742450585
0.930127051464864235179849855532211861819047738319
0.930009037736175803437119838800018142474577654648
0.930009034712565054788700692694508567400047032116
0.93000903471256505280413348817639994623615973968
0.93000903471256505280413348817639994538119999151
0.93000903471256505280413348817639994538119999151
0.93000903471256505280413348817639994538119999151
0.9300090347125650528041334881763999453811999915
还可以对牛顿迭代法改进一下：
http://mathworld.wolfram.com/HouseholdersMethod.html
http://mathworld.wolfram.com/HalleysMethod.html
若你安装了maple,只需修改附件中\(f0\)的值，依次对应值\(w,k,r,h,L\),重新计算即可（从上至下依次敲回车键即可得到）
\(t\)值和对应的函数图像\(g(t)=f(t)-f(0)-L\)