Question #139426
Find the root of the equation tanx + tanhx = 0 which lies in the interval (1.6, 3.0) correct to four significant digits using the method of false position.
1
Expert's answer
2020-10-22T17:25:15-0400

Given f(x)=tanx+tanhxf(x)=\tan x+\tanh x

f(a)=f(1.6)=tan(1.6)+tanh(1.6)=33.3109f(a)=f(1.6)=\tan(1.6)+\tanh(1.6)=-33.3109

f(b)=f(3)=tan(3)+tanh(3)=0.8525f(b)=f(3)=\tan(3)+\tanh(3)=0.8525

Using iterative Regula-Falsi Formula, the first approximation,


x1=abaf(b)f(a)f(a)=x_1=a-\dfrac{b-a}{f(b)-f(a)}f(a)==1.631.60.8525+33.3109(33.3109)=2.9324=1.6-\dfrac{3-1.6}{0.8525+33.3109}(-33.3109)=2.9324



f(2.9324)=0.7821f(2.9324)=0.7821


a=1.6,b=2.9324a=1.6, b=2.9324


x2=1.62.93241.60.7821+33.3109(33.3109)=2.9018x_2=1.6-\dfrac{2.9324-1.6}{0.7821+33.3109}(-33.3109)=2.9018

f(2.9018)=0.7495f(2.9018)=0.7495


a=1.6,b=2.9018a=1.6, b=2.9018


x3=1.62.90181.60.7495+33.3109(33.3109)=2.8732x_3=1.6-\dfrac{2.9018-1.6}{0.7495+33.3109}(-33.3109)=2.8732

f(2.8732)=0.7186f(2.8732)=0.7186


a=1.6,b=2.8732a=1.6, b=2.8732


x4=1.62.87321.60.7186+33.3109(33.3109)=2.8463x_4=1.6-\dfrac{2.8732-1.6}{0.7186+33.3109}(-33.3109)=2.8463

f(2.8463)=0.6891f(2.8463)=0.6891


a=1.6,b=2.8463a=1.6, b=2.8463


x5=1.62.84631.60.6891+33.3109(33.3109)=2.8211x_5=1.6-\dfrac{2.8463-1.6}{0.6891+33.3109}(-33.3109)=2.8211

f(2.8211)=0.6609f(2.8211)=0.6609

......


x149=2.36550x_{149}=2.36550

x150=2.36548x_{150}=2.36548

x151=2.36546x_{151}=2.36546

......


x499=2.36502x_{499}=2.36502

Root of f(x)f(x) is 2.3652.365



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