MATH 1571H SAMPLE MIDTERM II PROBLEMS
... The midterm exam will cover the Sections 3.1 - 3.6, 4.1 - 4.6 1. The sum of two positive numbers is 36. What is the smallest possible value of the sum of their squares? 2. Find the global maximum and global minimum of the function f (x) = 2x3 − 3x2 − 12x on the closed interval [−2, 3]. Find the inte ...
... The midterm exam will cover the Sections 3.1 - 3.6, 4.1 - 4.6 1. The sum of two positive numbers is 36. What is the smallest possible value of the sum of their squares? 2. Find the global maximum and global minimum of the function f (x) = 2x3 − 3x2 − 12x on the closed interval [−2, 3]. Find the inte ...
Chapter 2: Functions and Their Graphs
... We see that each x input is assigned exactly one y output. x is called the independent variable and y is called the dependent variable because its assigned value depends on x. Determine whether the following equations represent functions: a. x2 + y = 4 b. x2 + y2 = 4 ...
... We see that each x input is assigned exactly one y output. x is called the independent variable and y is called the dependent variable because its assigned value depends on x. Determine whether the following equations represent functions: a. x2 + y = 4 b. x2 + y2 = 4 ...
Function of several real variables
In mathematical analysis, and applications in geometry, applied mathematics, engineering, natural sciences, and economics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The ""input"" variables take real values, while the ""output"", also called the ""value of the function"", may be real or complex. However, the study of the complex valued functions may be easily reduced to the study of the real valued functions, by considering the real and imaginary parts of the complex function; therefore, unless explicitly specified, only real valued functions will be considered in this article.The domain of a function of several variables is the subset of ℝn for which the function is defined. As usual, the domain of a function of several real variables is supposed to contain an open subset of ℝn.