1) False .
Gradient of scalar function is always vector ..
Here
Fx = 2x
Fy = 2y
Gradient F= Fx I + Fy j = 2xi + 2yj
(2) false
Gradient gives the direction of maximum rate of change of function it can bhi positive or negative
(3) false
Gradient of above function has 3 Component
Gradient F = Fxi +Fyj + Fzk
(4) .True
Gradient F = Fx i + Fy j + Fz k = 0+0+0= 0
67. Explain why or why not Determine whether the following state- ments are true and give...
any help would be awesome Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. The sum Σ is a p-series. b. The sumeve IS a p-series. c. Suppose f is a continuous, positive, decreasing function, for re l'and ak =f(k), for k = 1,2,3, . . . . If Σ@g converges to L, then | f(x) dx converges to L. d. Every partial sums, of the series Σ underestimates...
State whether the following is always true (T) or not always true (F) a)V (4X − 2Y ) = 16V (X) + 4V (Y ) + 8Cov(X, Y ) b)If X1, X2, ..., X100 are independent, normally distributed random variables, then the average X¯ = 1 100Σ 100 i=1Xi of these random variables is itself a random variable following a normal distribution. c) If X and Y are random variables with a correlation of ρxy, Corr(2X, Y ) = 2ρxy
ECON 1111A/B Mathematical Methods in Economics II 2nd term, 2018-2019 Assignment 6 Show your steps clearly Define the definiteness of the following A-[1 5 a. b. 1 4 6 d. D= -2 3 1 -2 1 2 E 2 -3 1 2. Is the function f(x,y) - 7x2 + 4xy + y2 positive definite, negative definite, positive semidefinite or negative semidefinite? Find the extreme values for the following functions and identify whether they are local maximum, local minimum, and saddle...
For each relation below, determine the following.(i) Is it a function? If not, explain why not and stop. Otherwise, answer part (ii).(ii) What are its domain and image? (a){(x, y) :x, y∈Z, y- 2x}. (b){(x, y) :x, y∈Z, xy- 0}. (c){(x, y) :x, y∈Z, y-x2}. (d){(x, y) :x, y∈Z, x|y}. (e){(x, y) :x, y∈Z, x+y= 0}. (f){(x, y) :x, y∈R, x2+y2= 1}.
true or false is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
Exercise 1. Tangent plane (15 pts) Let (5) be the surface given by the following equation. x2+y2 = 1+z2 An equation of the tangent plane to (S) at A(1,2,2) is: a. 2x + 4y – 4z = 1 b. x + y - z=0 c. x + 2y – 2z = 1 d. x + y - z = 2 e. None of the above a. b. C. O d. e. Exercise 2. Directional derivative (6 pts + 9 pts)...
Determine the direction in which f(x, y, z) = x2 + y2 + x2 + xyz has a maximum rate of increase from the point (1,-1,1). Also determine the value of the maximum rate of increase at that point.
Only the Matlab part !!! Question 2 For the following vector fields F determine whether or not they are conservative. For the conservative vector fields, construct a potential field f (i.e. a scalar field f with Vf - F) (a) F(z, y)(ryy,) (b) F(z, y)-(e-y, y-z) (c) F(r, y,z) (ry.y -2, 22-) (d) F(x, y, z)=(-, sin(zz),2, y-rsin(x:) Provide both your "by hand" calculations alongside the MATLAB output to show your tests for the whether they are conservative, and to...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
For each of the statements below, state whether it is true or false. If true, explain why each of its directions → and ← is true. If false state which direction is false and give a counterexample. (a) ∀x (A(x) ∨ B(x)) ↔ ∀xA(x) ∨ ∀xB(x) (b) ∀x (A(x) ∧ B(x)) ↔ ∀xA(x) ∧ ∀xB(x) (c) ∃x (A(x) ∨ B(x)) ↔ ∃xA(x) ∨ ∃xB(x) (d) ∃x (A(x) ∧ B(x)) ↔ ∃xA(x) ∧ ∃xB(x)