Final answer:
To estimate the value of π and determine the number of throws for different error limits, you can use a Monte Carlo method.
Step-by-step explanation:
To estimate the value of π, you can use a Monte Carlo method, where you randomly throw darts at a square that encloses a circle. The ratio of darts that land inside the circle to the total number of darts thrown can be used to estimate π.
To determine the number of throws required for different error limits, you need to keep throwing darts until the estimated value of π falls within the desired error limit. For example, if the error limit is 0.5, you would keep throwing darts until the absolute difference between the estimated value of π and the true value of π is less than or equal to 0.5.
Comparing the performance of the machine for different error limits can provide insights into the trade-off between accuracy and computational time.