Answer to Question #331460 in Calculus for Ayeeshaaaa

Question #331460

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.


1
Expert's answer
2022-04-21T11:40:58-0400

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)" .


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