Lachlan's question via email about the Bisection Method

Prove It

Well-known member
MHB Math Helper
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.

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