A is the point (-1, 5). Let (x, y) be any point on the line y = 3x. a Write an equation in terms of x for the distance between (x, y) and A(-1,5). b Find the coordinates of the two points, B and C, on the line y = 3x which are a distance of √74 from (-1,5). c Find the equation of the line l1 that is perpendicular to y = 3x and goes through the point (-1,5). d Find the coordinates...
Let V = R2 with the following operations: (zı, yı) + (2 2,32) = (x1 +T2-1, yı +B2) (addition) c(x1, y) = (czi-e+ 1, cy) where c E R (scalar multiplication). Then V is a vector space with these operations (you can take this as given). (a) (2) Let (-2,4) and (2,3) belong to V and let c -2 R. Find ca + y using the operations defined on V. (b) (2) What is the zero vector in V? Justify....
Find the extreme values of the function f(x, y) = 3x + 6y subject to the constraint g(x, y) = x2 + y2 - 5 = 0. (If an answer does not exist, maximum minimum + -/2 points RogaCalcET3 14.8.006. Find the minimum and maximum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.) f(x, y) = 9x2 + 4y2, xy = 4 fmin = Fmax = +-12 points RogaCalcET3 14.8.010. Find...
(1 point) Suppose f (r,y)= P = (1, -2) and v=3i - 3j. A. Find the gradient of 1 Uf = 1 it -x/y^2 Note: Your answers should be expressions of x and y, eg "3x - 4y" j j B. Find the gradient off at the point P. (VA)(P) = 1 i+ -2 Note: Your answers should be numbers C. Find the directional derivative off at P in the direction of v. Duf = 9 Note: Your answer should...
Let a DT system described by the following difference equation: y[n]-5/6y[n-1]-1/6y[n-2]=1/6x[n-1] Find the zero input and zero state responses of this system for n≥0 assuming that the input s x[n]=2^nu[n] and the initial conditions y[-1]=1 and y[-2]=2.
SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY THE CRAMER'S METHOD 3X+5Y+3Z-12 2X+5Y-2Z-6 3x+6Y+3Z-3 a) X Y b) CHECK YOUR RESULTS. (USE MATRICE FUNCTIONS, PRESS F2. AND THEN PRESS CTRL+SHIFT+ENTER) 3IF Y-SINC) EXPOO. INTEGRATE Y FROM X-0 Tox-1. COMPARE WITH REAL VALUE IF DX-0 a) INT b) INT ,IF DX- 005 REAL VALUE 3) Plot sin x letting maco c/ Prepave hese cuves 4) SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY INVERSE METHOD 3 X+3Z-13 2X +5 Y-2Z-2 3 X+6Y+2Z-3 Z-...
1. Let f(x,y) = (2-7-% and g(x,y) = v f(x,y). J(1)(4 points) Find the maximum value of g(y). |(272 points) At which point(s) (x,y) and in the direction of which unit vector(s) ů does the maximum value for the directional derivative Dif(x,y) occur?
Let Select all that apply Let z =f(x,y)= arctan(3x In(6) Select all that apply Your answer: The slope of the tangent line to the curve obtained by intersecting the 9 surface z =f(x,y) and plane x = 3 at the point (3,6) is 6(811n (36) + 1) + fxy 54x2In(6y)+3) y(18x2in(6) + 1)2 (fxx (4,2))-(fvx(4,2)) = 0 The slope of the tangent line to the curve obtained by intersecting the 3In(36) surface z = f(x,y) and plane x = 3 at...
-2 (1 point) Express the vector v= -6 as a linear combination of x = 5 and - -23 y. x+
1. 2. (1 point) Let f(x,y,z) = 4x2 + xy + yz +5z?. Find the linearization L(x, y, z) of f(x,y,z) at the point (-1, -3, -1). L(x,y,z) = -5x-2y+72-3 Find an upper bound for the magnitude El of the error in the approximation f(x, y, z) ~ L(x, y, z) over the box |x +11 30.04, \y +31 < 0.04, 12 +11 30.04. E 3 (1 point) Let f(x, y) = 3 In(x) +2 In(y). Find the linearization L(av)...