Functions III
... Worked Example 2: Your task is to plot the key features of the given parabola, sketch the parabola, then state clearly its domain and range. Sketch the parabola f(x) = 15 - 2x - x2, hence state clearly its domain and range. Step 1: Determine concavity: Up or Down? For the parabola of the form f(x) ...
... Worked Example 2: Your task is to plot the key features of the given parabola, sketch the parabola, then state clearly its domain and range. Sketch the parabola f(x) = 15 - 2x - x2, hence state clearly its domain and range. Step 1: Determine concavity: Up or Down? For the parabola of the form f(x) ...
Nonconvex Optimal Control Problems with Nonsmooth Mixed State
... nonsmooth analysis. Let A ⊂ Rk be a closed 1 a.e., such that the following condition set with x̄ ∈ A. The limiting normal cone to A is satisfied for almost every t ∈ [0, 1], all at x̄ is denoted by NA (x̄). Given a lower semi(x, u) ∈ Tδ (t) × Uδ (t) for which g(t, x, u) > continuous function f : Rk ...
... nonsmooth analysis. Let A ⊂ Rk be a closed 1 a.e., such that the following condition set with x̄ ∈ A. The limiting normal cone to A is satisfied for almost every t ∈ [0, 1], all at x̄ is denoted by NA (x̄). Given a lower semi(x, u) ∈ Tδ (t) × Uδ (t) for which g(t, x, u) > continuous function f : Rk ...
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.