QUESTION 1 Let V-L2([0,1 ],C) and > : Vx-СУч . Г f(x)g(x)dx be an inner product...
Let h(x) = 14), where f(x) = –2x – 3 and g(x) = x2 – x + 2. What is h' (x)? Select the correct answer below: 2x2 +6x–7 *4–2x3 +5x2–4x+4 -6x2–2x-1 x+-2x3 +5x2-4x+4 2x2+6x–7 x-x+2 O za
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Example 11.2b Let us reconsider Example 11.2a, where we have 5 to invest among three projects whose return functions are f(x) = 2x . 1+x f(x) = 10( I-e-x). Let xi (j) denote the optimal amount to invest in project 1 when we have maxlfi(l), f2(1), f3(1))-max(5, 1632 6.32, a total of j to invest. Because we see that Xi(1)=0, X2(I) = 0, x3(1)=1. Since max(f(xdl) + I)-f(xdl)) = max(5, I, 8.65-6.32) = 5. we have X1(2)...
Question 14 Given f(x) = – 2x – 1 and g(x) = V2 – 9, find f (g-1(x)) = Submit Question x Question 15 Score on last try: 0 of 5 pts. See Details for more. Try a similar question You can retry this question below Let f(x) = 4 + vx – 4. Find f-1(x). f-1(x) = Now for fun, verify that (fo f-1)(x) = (f-10 f)(x) = = 2 Submit Question
(1 point) Use the inner product 1 0 <fig >= f(x)g(x)dx in the vector space Cº[0, 1] to find the orthogonal projection of f(x) = 6x2 + 1 onto the subspace V spanned by g(x) = x – į and h(x) = 1. projy(f) =
Problem 1. Let the inner product (,) be defined by (u.v)xu (x)v (x) dx, and let the norm Iilbe defined by lIul-)Corhe target funtio), and work with the approximating space P4 Use Gram-Schmidt orthogonalization with this inner product to find orthogonal polynomials (x) through degree four. Standardize your polynomials such that p: (1) 1. (a) Form the five-by-five Gram matrix for this inner product with the basis functions p (x) degree 4 approximation o f (x) using the specified norm,...
7. Let V = Pa(R), the vector space of polynomials over R of degree less than 2, with inner product Define φ E p by φ(g)-g(-1) a) By direct calculation, find f e V such that (S)-dg). You are given that A 1, V3-2v) is an orthonormal basis for V (you do not need to check this). b) Find the same f as in part a, using the formula for A(6) from class.
7. Let V = Pa(R), the vector...
us equation, L (y(x))-0. Prove that o a solution eneous equation, C(y(z))g(z). Is a hy or why not? 1. Let C be the linear operator defined as follows. (a) Let v,.. ,n be the solutions of the homogeneous equation, D an arbitrary linear combination, ciyi+..nn is also a solution. , c(y(z)) 0, Prove that (b) Let vi,. n be the solutions of the non-homogeneous equation, Cl) ga). Is a linear combination, ciy nyn also a solution? Why or why not?...
Question 1 V g(x) O a Let g)-IOdt, where asx Sb. The figure above shows the graph of g on [a.t]. Which of the following could be the graph of f on [a,b]? (B) y (A) Y 0 ct (E) Y D) Question 2 100 12 18 24 Hours The flow of oil, in barrels per hour, through a pipeline on July 9 is given by the graph shown above. Of the following, which best approximates the total number of...