Pick any exercise in Chapter 12 of the calculus textbook. Post the solution or your attempt. Discuss any issues you might have had. What were the most valuable elements you took away from this course?

Exercise 7-14: Give the domain and range of the multivariable function.

  1. f(x,y) = x - 2y

Domain is all real numbers for both x and y. Range is all real numbers.

  1. f(x,y) = 1/(x + 2y)

Domain is any real number x, y except x + 2y = 0. Range is all real number except 0.

  1. f(x,y) = 1/ (x^2 + y^2 + 1)

Domain is any real number x, y. Range is greater than 0 and less than or equal to 1.

  1. f(x,y) = sin(x) cos(y)

Domain is any real number x, y. Range for sin(x) is -1 to 1. Range for cos(x) is -1 to 1. So, range for sin(x)cos(x) is -1 to 1.

  1. f(x,y) = sqrt(9 - x^2 - y^2)

Domain is any x, y where x^2 + y^2 <= 9 (can’t take square root of negative number). Range is >= 0 and <= 3. When x = y = 0, value is 3, which is max.