3.1 Determine which of the following forces are conservative by find- ing the curl: (a) F...
Ex: Let F = -y it i } in R²: a) Find Curl F. b) is a conservative or not? c) Find a potential such that F= 8 d) calculate SE. dr :
Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl F Show steps (1 point) Let F (8y2)i(7xz)j+(6y) k Compute the following: A div F В. curl F- i+ k C, div curt F= Note: Your answers should be expressions of x, y and/or z; e.g. "3xy" or "z" or 5 (1 polnt) Consider the vector field F(r,y, ) = ( 9y , 0, -3ry) Find the divergence and curl of F div(F) VF=...
For each of the following vector fields, find its curl and determine if it is a gradient field. (1 point) For each of the following vector fields, find its curl and determine if it is a gradient field. (a) F = 5(xy + 22) + 10(x2 + y2) 7+ 10(x2 + y2) k. curl F = F ? (b) Ğ = 5yzi + (52z+z2) 7+ (5xy + 2yz) k: curl Ĝ = Ğ ? (c) H = (5xy + yz)...
1. One of the two vector fields listed below is conservative. The other one is not conservative. (a) Determine which one of these fields is conservative. Label the conservative field F and and find a potential function f for it. Label the other field G and prove that G is NOT conservative. (b) Use the fundamental theorem of line integrals to compute SCF . dr, where C is the curve parameterized by (c) Compute Jc G-dr, where C is the...
3. Consider the functions \(f(x, y, z)=x y z\) and \(\mathbf{F}(x, y, z)=y z^{2} i+x^{2} z j+x y^{2} k\). Determine which of the following operations can be carried out and find its value:div \(f, \operatorname{grad} f,\) div \(\mathbf{F},\) curl div \(\mathbf{F}\) and div curl \(\mathbf{F}\).
Determine if the following vector fields F: 2 CR" + R" are conservative. In case they are conservative, find a potential function f, that is, such that F= Vf. a) F(1, y) = (x²y, zy), N=R? b) F(1, y, z) = (ze", 22 sin(z), 2+z+1), N=R3 c) F(x,y) = (e cosy, -efsiny), R=R2
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...
Problem 3. Given: f(t) 3 -22 f(t) 0 otherwise 3.1 Determine which one of the following expressions is the (a) (1.5jw) (ee (b) (3/jw) (e -e Fourier transform for f: jw -jw jw) (e e 1.5jw 1.5jw (d) Bjw) (e (e) (2jw) (ee) 3.2 Rewrite F(w) as as a trigonometric sinusoidal function and sketch its wavefom. 3.3 Determine the values of first two frequency terms (w1 and w2) where F(w)-0. 3.4 Determine the inverse Fourier transform of f(t) and sketch...
Given F(x, y) = (x²y3, xy). (a) Determine if F is conservative. If yes, find the scalar potential. (b) Evaluate F.dr where is the path defined parametrically by r(t) = (13 – 2t, t3 + 2t) e/F c for 0 < t < 1.
Problem 7. Given that each of the following vector fields F is conservative Find a potential function f such that f = F and evaluate fe F dr along the given curve C 1. F(r,y) y C: F(t)(t3- 2t, t3 + 2t), 0 <t<1 2. F(x,y, ) yze"* i + e#* j + xye k C: F(t)(t2 1)i +(2 -1)( -2t)k, 0t 2