let two vectors be a(t) = e^t i + (sin 2t) j + t^3 k and b(t) = (e^-t , cos 3t, - 2 t^3) in euclidean three space R^3. Find d/dt [a(t) * b(t)].
let two vectors be a(t) = e^t i + (sin 2t) j + t^3 k and b(t) = (e^-t , cos 3t, - 2 t^3) in euclidean three space R^3. Find d/dt [a(t) * b(t)].
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2 2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
(1 point) Given the acceleration vector a(t) = (-4 cos (2t))i + (-4 sin (2t))j + (-3t) k , an initial velocity of v (0) =i+ k, and an initial position of r (0)=i+j+ k, compute: A. The velocity vector v (t) = j+ . B. The position vector r(t) = j+ k
(1 point) Starting from the point (4,3,2)(4,3,2) reparametrize the curve r(t)=(4+3t)i+(3−3t)j+(2−2t)kr(t)=(4+3t)i+(3−3t)j+(2−2t)k in terms of arclength.
Find the curvature of r(t) = (-7 sin(t), cos(2t), –3t) at t = ž. (Use symbolic notation and fractions where needed.) k () =
find T,N,B curvature and torsion as a function of t for the space curve r(t)=sin t i+√2 cos t j+sin t k and find equation of normal and osculating planes
2. Find the Laplace transform of the following functions (a) f(t)3t+4 (b) cos(2Tt) (c) sin(2t T) (d) sin(t) cos(t) "Use Trig. Identity" (e) f(t) te 2t use first shifting theorem
' cos(3t), t<n/2, 2. Let f(t) = sin(2t), 7/2<t< , Write f(t) in terms of the unit step e3 St. function. Then find c{f(t)}.
all parts -2t e - (13 points) Let f(t) cos 2t, sin 2t) for t 2 0. F() (a) (4 points) Find the unit tangent vector for the curve d (F(t)-v(t)) using the product rule for dt (b) (5 points) Let v(t) = 7'(t). Calculate the dot product and simplify v(t) (c) (4 points) For an arbitrary vector-valued function 7 (t) with velocity vector = 1, what can be said about the relationship between F(t) and v(t)? if F(t) (t)...
(1 point) Given R(t)=e4tcos(3t)i+e4tsin(3t)j+3e4tkR(t)=e4tcos(3t)i+e4tsin(3t)j+3e4tk Find the derivative R′(t)R′(t) and norm of the derivative. R′(t)=R′(t)= ∥R′(t)∥=‖R′(t)‖= Then find the unit tangent vector T(t)T(t) and the principal unit normal vector N(t)N(t) T(t)=T(t)= N(t)=N(t)= (1 point) Given R(t) = cos(36) i + e sin(3t) 3 + 3e"k Find the derivative R') and norm of the derivative. R'(t) = R' (t) Then find the unit tangent vector T(t) and the principal unit normal vector N() T(0) N() Note: Yn can can on the hom
e-27 2. Calculate L et sint+e-2t cos st sint+e-2 cos 3t+t%e3+ + ✓at ec [e*sin U2n(t) sin 2t sin 21