Question

Find the work done by F(x,y)= <3x^2y+1, x^3+2y> in moving a particle from P(1,1) to Q(2,4) across the curve y=x^2. Please explain your steps. ````

Answer #1

1) Find the arclength of y=4x+3 on 0≤x≤3
2) Find the arclength of y=3x^3/2 on 1≤x≤3
3) The force on a particle is described by 5x^3+5 at a point xx
along the x-axis. Find the work done in moving the particle from
the origin to x=8
4) Find the work done for a force F =12/x^2 N from x =2 to x =3
m.
5) A force of 77 pounds is required to hold a spring stretched
0.1 feet beyond...

Evaluate ∫_0,3^2,4▒〖(2y+x^2 )dx+(3x-y)dy along〗 The parabola
x=2t, y=t^2 +3 Straight lines from (0,3) to (2,3) A straight line
from (0,3) to (2,4)

find the work done in the force camp F(x,y,z)=<xz,xy,zy> in a
particle that moves along the curve <t^2,-t^3,t^4> for 0
<= t <= 1
THE
F is F(x,y,z)= <xz,yx,zy>

Let f(x,y) = 3x^2y − 2y^2 − 3x^2 − 8y + 2.
(i) Find the stationary points of f.
(ii) For each stationary point P found in (i), determine whether
f has a local maximum, a local minimum, or a saddle point at P.
Answer:
(i) (0, −2), (2, 1), (−2, 1)
(ii) (0, −2) loc. max, (± 2, 1) saddle points

Find the work done in moving a particle once around an ellipse C
in the xyplane, if the ellipse has center at the origin with
semi-major axis p and semi-minor axis 2p and if the force field is
given by F⃗ = (3x − 4y + 2z)i + (4x + 2y − 3z2)j + (2xz − 4y2 +
z3)k⃗

Q 1) Consider the following functions.
f(x) = 2/x, g(x) = 3x + 12
Find (f ∘ g)(x).
Find the domain of (f ∘ g)(x). (Enter your answer using interval
notation.)
Find (g ∘ f)(x).
Find the domain of (g ∘ f)(x). (Enter your answer using
interval notation.)
Find (f ∘ f)(x).
Find the domain of (f ∘ f)(x). (Enter your answer using
interval notation.)
Find (g ∘ g)(x).
Find the domain of (g ∘ g)(x). (Enter your answer using interval
notation.)
Q...

Let X and Y have a joint density function given by f(x; y) = 3x;
0 <= y <= x <= 1
(a) Find P(X<2Y).
(b) Find cov(X,Y).
(c) Find P(X < 1/2 |Y = 1/3).
(d) Find P(X = 1/2|Y = 1/3).
(e) Find P(X > 1/2|Y > 1/3).
(f) Find the conditional expectation E(X|Y = y).

The real part of a f (z) complex function is given as
(x,y)=y^3-3x^2y. Show the harmonic function u(x,y) and find the
expressions v(x,y) and f(z). Calculate f'(1+2i) and write x+iy
algebraically.

Please show all the work.
1. Consider the following curve f(x)=3x^4-16x^3+24x^2-9. Find
the coordinates of the minimum.
2. The curve y=x^3+kx^2 +2x-1 has a point of inflection at x=-3
Find the value of k.
3. Find the equation of the perpendicular line of the curve
x^3+y^3=4y^2 at the point (2,2)
4. Alina invested $20,000 in a mutual find, and after 8 years,
her original has tripled. Find use the P(t)=P0e^rt
a. Find the yearly percentage growth rate
b.The rate of the...

Find the parameterization of the function y= x^2 from (2,4) to
(10,100). Then find the length of the parameterized curve. [SHOW
ALL WORK]

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