Problem 10 For each part below, a function f and a point P are given. Let 0 represent the direction of the directional derivative, i.e. the angle between the unit vector and the positive x-axis. Complete the following: (a) Write the directional derivative at P as a function of 0; call this function g. (b) Find the value of 0 that maximizes g(0) and find the maximum value. (c) Verify that the value of 0 that maximizes g corresponds to the direction of the gradient, and the maximum value of g equals the magnitude of the gradient. 1. f(x,y) = 10 – 2x² – 3y²; P(3, 2) 2. f(x, y) = In (1 + 2x² + 3y²); P(¿,-V3)

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A:

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.