Question

Use the bissection method to approximate the root of f(x)=2x^2-1 in the interval (0,1). Let ε =0.1be the margin of error of approximation.0.1be the margin of error of approximation.

Answer 1

The initial interval is $(0,1)$ and $f(0)=-1, f(1)=1$ .

Step 1: $m=(0+1)/2=0.5$ and $f(m)=f(0.5)=-0.5.$ New interval is $(0.5,1)$

Step 2: $m=(0.5+1)/2=0.75$ and $f(m)=f(0.75)=0.125$ New interval is $(0.5,0.75)$

Step 3: $m=(0.5+0.75)/2=0.625$ and $f(m)=f(0.625)=-0.21875$ New interval is $(0.625,0.75)$

Step 4: $m=(0.625+0.75)/2=0.6875$ and $f(m)=f(0.6875)=-0.0546875$ New interval is $(0.6875,0.75)$

Since $0.75-0.6875=0.0625<0.1$

which is the margin of error, we can stop the approximation.

The root is in the interval $(0.6875,0.75)$ .