Question

In: Math

Integration of the vector function: F(t) =et.sin2ti + t2j + t2.e2tk

Integration of the vector function: F(t) =et.sin2ti + t2j + t2.e2tk

Solutions

Expert Solution


Related Solutions

Consider the following vector function. r(t) =<3t, 1/2 t2, t2> (a) Find the unit tangent and...
Consider the following vector function. r(t) =<3t, 1/2 t2, t2> (a) Find the unit tangent and unit normal vectors T(t) and N(t). (b). Find the curvature k(t).
The position vector F(t) of a moving particle at time t[s] is given by F(t)= e^t...
The position vector F(t) of a moving particle at time t[s] is given by F(t)= e^t sin(t)i-j+e^t cos(t)k a) Calculate the acceleration a(t). b) Find the distance traveled by the particle at time t = 3π/2, if the particle starts its motion at time t = π/2. c) Find the unit tangent vector of this particle at time t = 3π/2. d) Find the curvature of the path of this particle at time t = 3π/2.
A vector y  =  [R(t)  F(t)]T describes the populations of some rabbits R(t) and foxes F(t). The...
A vector y  =  [R(t)  F(t)]T describes the populations of some rabbits R(t) and foxes F(t). The populations obey the system of differential equations given by y′  =  Ay where A  =  [−2 15] [−2 9 ] The rabbit population begins at 6000. If we want the rabbit population to grow as a simple exponential of the form R(t)  =  R0e3t  with no other terms, how many foxes are needed at time t  =  0? (Note that the eigenvalues of A...
A vector y  =  [R(t)  F(t)]T describes the populations of some rabbits R(t) and foxes F(t). The...
A vector y  =  [R(t)  F(t)]T describes the populations of some rabbits R(t) and foxes F(t). The populations obey the system of differential equations given by y′  =  Ay where A  =  146 −1656 12 −136 The rabbit population begins at 84000. If we want the rabbit population to grow as a simple exponential of the form R(t)  =  R0e8t  with no other terms, how many foxes are needed at time t  =  0? (Note that the eigenvalues of A are...
If the moment-generating function of X is M(t) = exp(3 t + 12.5 t2) = e3...
If the moment-generating function of X is M(t) = exp(3 t + 12.5 t2) = e3 t + 12.5 t2. a. Find the mean and the standard deviation of X. Mean = standard deviation = b. Find P(4 < X < 16). Round your answer to 3 decimal places. c. Find P(4 < X2 < 16). Round your answer to 3 decimal places.
f(t) = 1- t 0<t<1 a function f(t) defined on an interval 0 < t <...
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
Consider the following. optimize f(t, w) = 5t − t2 + 2w − w2 subject to...
Consider the following. optimize f(t, w) = 5t − t2 + 2w − w2 subject to g(t, w) = 2t + w = 14 (a) Write the Lagrange system of partial derivative equations. (Enter your answers as a comma-separated list of equations. Use λ to represent the Lagrange multiplier.) (b) Locate the optimal point of the constrained system. (t, w, f(t, w)) =    (c) Identify the optimal point as either a maximum p
Find the Laplace transforms: F(s)=L{f(t)} of the function f(t)=(8−t)(u(t−2)−u(t−5)), for s≠0. F(s)=L{f(t)}=
Find the Laplace transforms: F(s)=L{f(t)} of the function f(t)=(8−t)(u(t−2)−u(t−5)), for s≠0. F(s)=L{f(t)}=
Given y 1 ( t ) = t2 and y2 ( t ) = t ^−...
Given y 1 ( t ) = t2 and y2 ( t ) = t ^− 1 satisfy the corresponding homogeneous equation of t^2 y ' ' − 2 y = − 3 − t , t > 0 Then the general solution to the non-homogeneous equation can be written as y ( t ) = c1y1(t)+c2y2(t)+yp(t) Use variation of parameters to find y p ( t ) .
6. The function f(t) = 0 for − 2 ≤ t < −1 −1 for −...
6. The function f(t) = 0 for − 2 ≤ t < −1 −1 for − 1 ≤ t < 0 0 for t = 0 1 for 0 ≤ t < 1 0 for 1 ≤ t ≤ 2 can be extended to be periodic of period 4. (a) Is the extended function even, odd, or neither? (b) Find the Fourier Series of the extended function.(Just write the final solution.)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT