Math Problem Statement

Given the function g(x, y) = 3x cos(x + y^2) (i) Using Mathematica, create a contour plot of g(x,y) for −4.5 ≤ x ≤ 4.5 and −2.5 ≤ y ≤ 2.5. Show 16 contours and create a key (a plot legend) next to your plot for the value of each contour. (ii) Using Mathematica, create a surface plot of z = g(x, y) for −4.5 ≤ x ≤ 4.5 and −2.5 ≤ y ≤ 2.5. Use the rotation tool in Mathematica to orient your surface to show its features as clearly as possible in your answer.

Solution

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Math Problem Analysis

Mathematical Concepts

Multivariable Calculus
Contour Plotting
Surface Plotting
Trigonometric Functions

Formulas

g(x, y) = 3x cos(x + y^2)

Theorems

Properties of Contour Plots
Properties of Surface Plots

Suitable Grade Level

College Level - Calculus