Understanding Functions of Two Variables

The video tutorial explains how to evaluate a function of two variables, specifically focusing on the function F(x,y) = e^(x*y) * x^2. It provides step-by-step calculations for evaluating the function at specific points, such as F(2,0) and F(2,3). The tutorial also discusses the difference between exact values and decimal approximations, using a calculator to find the approximate value of 4e^6. The video concludes with a reminder to use exact values unless instructed to round, and offers helpful tips for understanding the process.

What is the general form of the function discussed in the video?

• f(x, y) = x^2 - y^2

• f(x, y) = x^2 + y^2

• f(x, y) = e^(x*y) * x^2

• f(x, y) = e^(x+y) * y^2

When evaluating f(2,0), what is the value of e^(2*0)?

• 2

• 1

• 0

• 4

What is the final result of f(2,0)?

• 8

• 4

• 2

• 0

In the evaluation of f(2,3), what is the exponent in e^(2*3)?

• 3

• 4

• 6

• 5

What is the exact value of f(2,3) as calculated in the video?

• 4e^3

• 4e^6

• 2e^3

• 2e^6

What is the approximate decimal value of f(2,3) rounded to four decimal places?

• 3,141.5926

• 2,718.2818

• 1,000.1234

• 1,613.7152