Question

Show that

-e^(-t)(sint) +3/2cos^2tsinte^(-t) -e^(t)cost+3/2e^(-t)cos^2(t)sint

is equal to

-e^(-t)sint +e^(-t)cost

Answer #1

For problem 1 to 3, use r(t)= <e^2t cost, e^2t sint, e^2t>
to find each of the following at t = 0.
1, T(t)
2, N(t)
3, Curvature

y'+y cos t = y^2 te^ sint
Solve the equation

find t?
x= 2cos(t)+ sin(2t)
y=2sin(t)+cos(2t)
when x= 0, y= -3

1. y" + 2y' + y = e^(-t) cos(t)
2. y" + 4y' + 4y = t- 2e^(2t)

Find the length of the curve
1) x=2sin t+2t, y=2cos t, 0≤t≤pi
2) x=6 cos t, y=6 sin t, 0≤t≤pi
3) x=7sin t- 7t cos t, y=7cos t+ 7 t sin t, 0≤t≤pi/4

Find F(s). ℒ{(1 − e^t + 2e^−5t)cos 6t} F(s) =

Given the function f(t) = 1/2cos (pi/3 *t) +3pi^2. Which of the
following is equal to f'(t)
f'(t) = 1/2sin(pi/3 t) +6pi
f'(t) = -pi/3cos(pi/3 *t)
f'(t) = -pi/6 sin(pi/3 T)
f'(t) = pi/3 sin(pi/3 t) +6pit

Show that E(x,t) = Emax. Cos (kx – wt)
And B(x,t) = Bmax. Cos (kx – wt)
Are solutions to the Wave Equations

The curve given by the parametric equations of x = 1-sint, y = 1-cos t ,
Calculate the volume of the rotational object formed by rotating the x axis use of the parts between t = 0 and t = π / 2.
Please solve this question carefully , clear and step by step.I
will give you a feedback and thumb up if it is correct.

find the length of the curve r(t)=(tsint+cost)i+(tcost-sint)j from
t=sqrt(2) to 2

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