Lachlan's question via email about the Bisection Method

[Prove It]

Consider the equation $\displaystyle 8\cos{\left( x \right) } = \mathrm{e}^{-x/7} $.

Perform four iterations of the Bisection Method to find an approximate solution in the interval $\displaystyle x \in \left[ 1.35, 1.6 \right] $.

The Bisection Method is used to solve equations of the form $\displaystyle f\left( x \right) = 0 $, so we need to rewrite the equation as $\displaystyle 8\cos{ \left( x \right) } - \mathrm{e}^{-x/7} = 0 $. Thus $\displaystyle f\left( x \right) = 8\cos{ \left( x \right) } - \mathrm{e}^{-x/7} $.

I have used my CAS to solve this problem. Note that the calculator must be in Radian mode.

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So our solution is $\displaystyle x \approx c_4 = 1.45938 $.

 

[Svein]

I checked your calculations using Excel, and they agree. After a couple more iterations I get x≈1,4701171875.