1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2 If(x,y)| 〈 M(x2 + y2)· for all (a·y) E R2 Prove that: 1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2...
(e) Let x = (T1,T2, . . . ,xn),y=(y1,y2, . . . ,Un) ER" (i) Show that for any λ E R: 3 where llxll = 1/(x, x). x, y (ii) Use (7) for λ =- to show: 1a1 with equality, if and only if, there exists a λ E R such that y = 1x.
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z. 4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z.
1. Find the absolute maximum and minimum values of f(r,y) = x2+y2+5y on the disc {(x, y) | x2+y2 < 4}, and identify the points where these values are attained 2. Find the absolute maximum and minimum values of f(x, y) = x3 - 3x - y* + 12y on the closed region bounded by the quadrilateral with vertices at (0,0), (2,2), (2,3), (0,3), and identify the points where these values are attained. 3. A rectangular box is to have...
4. A random point (X, Y ) is chosen uniformly from within the unit disk in R2, {(x, y)|x2+y2< 1} (a) Let (R, O) denote the polar coordinates of the point (X,Y). Find the joint p.d.f. of R and . Compute the covariance between R and 0. Are R and e are independent? (b) Find E(XI{Y > 0}) and E(Y|{Y > 0}) (c) Compute the covariance between X and Y, Cov(X,Y). Are X and Y are independent? 4. A random...
S-1. Consider the functions f: RR defined by f(x, y, 2) 2-y2- and g(r,y,) -2 Describe the sets of regular values of f and g, respectively. Which of the sets f-1(0), g(0), and g (1) are regular surfaces? Describe the images of f10), 0)\(0,0,0)), and g(1) under the Gauss-map. S-1. Consider the functions f: RR defined by f(x, y, 2) 2-y2- and g(r,y,) -2 Describe the sets of regular values of f and g, respectively. Which of the sets f-1(0),...
S1=(x, y, z) belongs to R^3,x^2+y2 =1 and s2=(x, y, z) belongs to R^3 and y=x find parametrization of intersection s1and s2
Which of the two mathematically equivalent expressions, 2 -y2 and (+) (-y), can be evaluated Which of the two mathematically equivalent expressions, r2y and (r+y) (r-y), can be evaluated more accurately in floating-poiandnt arithmetic? Why? For what values of r y, relative to each other, is there a substantial difference in the accuracy of the two expressions? (8 points) Which of the two mathematically equivalent expressions, 2 -y2 and (+) (-y), can be evaluated Which of the two mathematically equivalent...
Prove the following two statements. 1. If 30, Y ER, then the following initial value problem d'= -2(x2 + y2) y' = -4(x2 + y2) x(0) = 20 y(0) = yo has a solution for all t> 0 but not all t < 0 unless Xo = yo = 0. 2. If FE C'R" + R"), XO E R", \(X) is a curve in R", defined on R, satisfying the initial value problem X' = F(X) X(0) = Xo and...
Prove d2 is a metric d2 : R2 x R2 - R (r, y) max{a 2 - y2}.
Post an Article
Post an Answer
Post a Question
with Answer
Self-promotion: Authors have the chance of a link back to their own personal blogs or social media profile pages.