(1 point) If C is the curve given by
r(t)=(1+5sint)i+(1+3sin2t)j+(1+3sin3t)k, 0≤t≤π2 and F is the radial...
(1 point) If C is the curve given by
r(t)=(1+5sint)i+(1+3sin2t)j+(1+3sin3t)k, 0≤t≤π2 and F is the radial
vector field F(x,y,z)=xi+yj+zk, compute the work done by F on a
particle moving along C.
The curve C is given by the parameterization ⃗r(t) = <−t , 1
− t^2> for −1 ≤ t ≤ 1.
a) Choose any vector field F⃗ (x, y) = 〈some function , some other
function〉 and setup the work integral of F⃗ over C.
b)Choose any vector field G⃗(x,y) which has a potential function
of the form φ(x,y)= x^3 + y^3 + some other stuff and compute the
work done by G⃗ over C.
Please use a somewhat basic...
f(t) = 1- t 0<t<1
a function f(t) defined on an interval 0 < t < L is given.
Find the Fourier cosine and sine series of f and sketch the graphs
of the two extensions of f to which these two series converge
(1 point) For the given position vectors r(t)r(t) compute the
unit tangent vector T(t)T(t) for the given value of tt .
A) Let r(t)=〈cos5t,sin5t〉
Then T(π4)〈
B) Let r(t)=〈t^2,t^3〉
Then T(4)=〈
C) Let r(t)=e^(5t)i+e^(−4t)j+tk
Then T(−5)=
Given the following economy:
Y = C(Y - T) + I(r) + G
C(Y - T) = a + b(Y - T)
I(r) = c - dr
M/P = L(r,Y)
L(r,Y) = eY - fr
i. Solve for Y as a function of r, the exogenous variables G and
T, and the model's parameters a, b, c, and d.
ii. Solve for r as a function of Y, M, P, and the parameters e
and f.
iii. Derive the aggregate...
Consider the group G = {1, −1, i, −i, j, −j, k, −k} under
multiplication. Here
i2= j2= k2= ijk = −1. determine which of the following sets is a
subgroup
of G. If a set is not a subgroup, give one reason why it is
not.
(a) {1, −1}
(b) {i, −i, j, −j}
(c) {1, −1, i, −i}
(d) {1, i, −i, j}
Let f: [0 1] → R be a function of the class c ^ 2 that
satisfies the differential equation f '' (x) = e^xf(x) for all x in
(0,1). Show that if x0 is in (0,1) then f can not have a positive
local maximum at x0 and can not have a negative local minimum at
x0. If f (0) = f (1) = 0, prove that f = 0