localhost

File Edit View Run Kernel Settings

Help

B

$+$ X $$

$$ C

Markdown

this point. Depending on the sign of $($F$($c$)$ :

Jupyterlak

$$If $($f$($c$))$ is close to zero $($within the specified tolerance$),$ it returns $($ c$)$ as the root and the number of iterations taken.

$$If $($fla$))$ and $($ f$($c$))$ have opposite signs, it updates $($ b$)$ to $($ c$).$

$$Otherwise$,$ it updates $($a$)$ to $($ c $).$

$4.$ Stopping Condition: The loop continues until the function value at $($ c$)$ is within th specified tolerance or the maximum number of iterations is reached. If neither condition is met, a 'ValueEresult is printed.

Conclusion

This implementation of the Bisection Method provides a reliable way to find roots of continuous functions. You can easily modify the function and interval to explore differen scenarios.

$[16]$:

# Use of the function

bisection $\_$method$($lambda x: $**2-2,1,1\mathrm{.}5,0\mathrm{.}5)$

NameError

Cell In$[16],$ line $2$

$1$ # Use of the function

$-..->2$ bisection method$/$lambda $*$: x$**2-2\mathrm{.}1\mathrm{.}1\mathrm{.}5\mathrm{.}0\mathrm{.}51$

Traceback $($most recent call last$)$