You determine a function f(x) that passes through the points (x0, y0), (x1, y1),..., (xn, yn) with x0 < x1 < x2... xn. For some other point x * E (x0, xn), you then use f(x * ) to approximate the value of the actual smooth function that underlies the data. This procedure is called: O regression O extrapolation O curve fitting O interpolation

The question describes a function S(k) which is defined as the sum of the positive divisors of a positive integer k, minus k itself. The function S(1) is defined as 1, and for any positive integer k greater than 1, S(k) is calculated as S(k) = σ(k) - k, where σ(k) is the sum of all positive divisors of k. Some examples of S(k) are given: S(1) = 1 S(2) = 1 S(3) = 1 S(4) = 3 S(5) = 1 S(6) = 6 S(7) = 1 S(8) = 7 S(9) = 4 The question then introduces a recursive sequence a_n with the following rules: a_1 = 12 For n ≥ 2, a_n = S(a_(n-1)) Part (a) of the question asks to calculate the values of a_2, a_3, a_4, a_5, a_6, a_7, and a_8 for the sequence. Part (b) modifies the sequence to start with a_1 = k, where k is any positive integer, and the same recursion formula applies: for n ≥ 2, a_n = S(a_(n-1)). The question notes that for many choices of k, the sequence a_n will eventually reach and remain at 1, but this is not always the case. It asks to find, with an explanation, two specific…

Determine whether each of these functions is a bijection from ℝ to ℝ. If it is, write the inverse function. f(x) = 2x3-5

My apologies for misunderstanding. Here's the translation: "A function, f:f(x,y)=x2+2y2−12x+xy is defined on the domain: Ω = {(x, y): -1 ≤ x ≤ 1, -1 ≤ y ≤ x}. Create a contour plot of the function and plot the boundary of Ω with a dashed line: In Python