Let f : R2 + R be defined by f(L,y) = |kyle=(2²+y?). Evaluate /ik2 f, if...
Let f:R2→R be defined by f(x,y) =|xy|e−(x2+y2). Evaluate
∫R2f, if it exists
Let f : R2 + R be defined by f(L,y) = [tyle=(3++y?). Evaluate Sir2 f, if it exists
Let f: R2 + R be defined by f(x, y) = xyle=(22+y?). Evaluate Sr2 f, if it exists
Let f : R2 + R be defined by f(x,y) = |xy|e-(z?+y?). Evaluate SR2 f, if it exists
Let f: R2 + R be defined by f(x, y) = xyle=(22+v?). Evaluate Sg2 f, if it exists
5. Let f : R2 + R be defined by f(x,y) = xyle=(x2+zº). Evaluate Sr2 f, if it exists (8 points).
(b) Let F: R2 + Rº be a vector field on R2 defined as F(x, y) = (3y, 22 – y). Suppose further that ^ C R2 is a curve in R2 consisting of the parabola y = 22 - 1 for 1 € (-1,0) and the straight line y = 1 – 1 for 1 € [0,1]. (i) Sketch the curvey in R2 [2] (ii) By considering the curve y piecewise, compute the vector field integral: [5] F(x). F(x)...
1. Let L: R2-R2 be defined by L(x.y) (x +2y, 2x - y). Let S be the natural basis of R2 and let T = {(-1,2), (2,0)) be another basis for R2 . Find the matrix representing L with respect to a) S b) S and1T c) T and S d) T e) Find the transition matrix Ps- from T basis to S basis. f) Find the transition matrix Qre-s from S-basis to T-basis. g) Verify Q is inverse of...
1. Consider the unit circle: (x,y) : x2 y2 = 1. T. Let f R2 ->R be defined by f(x,y) = x2-y, and let F : R2 -> R be defined by F(x, y) Compute the integral of f and F around the unit circle. For the integral of F, proceed in the standard (anticlockwise) direction
I. Let f : R2 → R be defined by f(x)l cos (122) 211 Compute the second order Taylor polynomial of f near the point xo - 0. A Road Map to Glory (On your way to glory, please keep in mind that f is class C) a) Fill in the blanks: The second order Taylor's polynomial at h E R2 is given by T2 (h) = 2! b) Compute the numbers, vectors and matrices that went into the blanks...
please answer both a and b
Problem 2 (Eigenvalues and Eigenvectors). (a) If R2-R2 be defined by f(x,y) = (y,z), then find all the eigenvalues and eigenvectors of f Hint: Use the matrix representation. (b) Let U be a vector subspace (U o, V) of a finite dimensional vector space V. Show that there exists a linear transformation V V such that U is not an invariant subspace of f. Hence, or otherwise, show that: a vector subspace U-o or...