Answer to Question #183084 in Quantitative Methods for hamdoon

Question #183084

Find the smallest positive root by using the bisection method

2sin(2x)+2x^3-5


with 3 decimal plates

1
Expert's answer
2021-04-25T09:23:33-0400

Given,

"2x^3+2\\sin (2x)-5=0"

"\\Rightarrow f(x)=2x^3+2\\sin(2x)-5"

Now, x=0, 1, 2...

1st Iteration:

"f(1)=-1.1814<0" and "f(2)=9.4864>0"

Now, root lies between 1 and 2.

"x_o=\\frac{1+2}{2}=1.5"

"f(x_o)=f(1.5)=2*1.5^3+ 2\\sin(3)-5=2.0322>2"


2nd Iteration:

"f(1)=-1.1814<0"

and "f(1.5)=2.0322>0"

Root lies between 1 and 1.5

"x_1=\\frac{1+1.5}{2}=1.25"

"f(x_1)=f(1.25)=2*1.253+2\\sin(2.5)-5=0.1032>0"


3rd Iteration:

Here "f(1)=-1.1814<0" and "f(1.25)=0.1032>0"

Now, Root lies between 1 and 1.25

"x_2=\\frac{1+1.25}{2}=1.125"


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