Scientists create a futuristic soap bubble in the shape of a box with a square base that contains a fixed volume of air. Specifically, the soap bubble contains 3 cm³ of air. (a) Draw a picture. (b) If the base of the soap bubble box has a side length of 2 cm, what is the surface area of the soap bubble? (c) If the base of the soap bubble box has a side length of x cm, what is the surface area of the soap bubble? (d) Use differentials to approximate the change in surface area if the side length of the base is shrunk from 2 cm to 1.99 cm.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.