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QUESTION ar Solve д aF at at (x, t) = (1,0) for the given vector function,...
Evaluate the line integral ∫C.F·dr, where C is given by the vector function r(t).F(x, y, z) = sin(x) i + cos(y) j + xz k r(t) = t3 i- t3j + tk, 0 ≤ t ≤ 1 .
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Question 5 25 (5.1) Sketch some vectors in the vector field given by F(r, y) 2ri + yj. (3) (5.2) Evaluate the line integral fe F dr, where F(r, y, 2) = (x + y)i + (y- 2)j+22k and C is given by the vector function r(t) = ti + #j+Pk, 0 <t<1 (4) costrt>, 0St<1 (5.3) Given F(r, y) = ryi + yj and C: r(t)=< t + singat, t (3) (a) Find a function f such...
Evaluate the line integral ∫ F *dr
where C is given by the vector function
r(t).
F(x, y, z) =
(x + y2) i +
xz j + (y + z)
k,
r(t) =
t2i +
t3j − 2t
k, 0 ≤ t ≤ 2
Match each given vector equation with the corresponding curve. y4 0 b a (0, 1,0) (1,0,0 , 1,0 d C 2 A (0,0. 2 y- r(t)= (, ? r(t) (sin (t),t) r (t) (t, cos (2t), sin (2t)) ? v r (t) (1 +t,3t,-t) r (t) (t)i-cos (t)j+sin (t) k =COS r(t)=i+tj+k r(t) i+tj+2k r(t)= (1,cos (t).2sin (t)
Match each given vector equation with the corresponding curve. y4 0 b a (0, 1,0) (1,0,0 , 1,0 d C 2 A...
Solve the initial value problem for r as a vector function of t. dr Differential equation: of = -7t i-5t j - 3t k Initial condition: r(0) = 7i + 2+ 3k r(t) = (O i+();+ ( Ok
A particle's position as a function of time is described by the vector f(t) = x(1)i + y(t)j + z(t)k. • x(t) = 2.6 +3.06] + + 1.5 [m] • y(t) = 0 • z(t) = 6.3 [m] (cos(ot) + sin(wt)) At a time t = 6.8s, for o=1.1, what is a(DI? Answer in meters per second squared ).
a) Find the length of the curve traced by the given vector function on the indicated interval: r(t)e' costie' sin tj+e'k 0<t<In2 b) Find the gradient of the scalar function f 6xyz + 2x+ xz at (1, 1, -1) c) Find the curl of the given vector field: F(x, y,z) 4xyi + (2x2 +2yz)j+(3z2+y2)k
The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H) + K. where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(z) into g(x) where the transformation is g(x) = -f(x) The function f(s) is shown below...
Let H=F(x,y) and x=g(s,t), y=k(s,t) be differentiable functions. Now suppose that g(1,0)=8, k(1,0)=4, gs(1,0)=8, gt(1,0)=2, ks(1,0)=1, kt(1,0)=5, F(1,0)=9, F(8,4)=3, Fx(1,0)=13, Fy(1,0)=7, Fx(8,4)=9, Fy(8,4)=2. Find Hs(1,0), that is, the partial derivative of H with respect to s, evaluated at s=1 and t=0.
Question 2 Find T(t) and N(t) at the given point. x= e cost, y = e sint, z=e; t = 0 and the vector k as Enter the vector i as 7, the vector j as , T(0) = Edit N(0) = Edit