H=1.68 T=26 F=2 L=2 S=30 11) Determine the extrema of g(u,v) = Hu-(F+L)t/2 subject to the...
T=20, S=60, H=6, L=3, F=3 Alls. 10). Given the shaded region to the right, determine the area using integration as follows: A. SSdxdy Ans. S B. SSdydx Ans. T/2 c. Sſrdrdo Ans. 1/2 SV2 11) Determine the extrema of g(u,v) = Hu-(F+L)t/2 subject to the constraint x2+y2= S*H Ans. 12) Evaluate S zyx ds where C is the vector r(t)=<sin(Ft), cos(-Ft), (T)t>; asts Hit с Ans.
H=1.68 T=26 F=2 L=2 S=30 10) Given the shaded region to the right, determine the area using integration as follows: A. SSdxdy Ans. S B. SSdydx Ans. T/2 X C. Sſrdrde Ans. T/2 SVE
In 11,) Find = classify any relative extrema Of f(x,y)=2x² 4 xy + 2 / 4 g 12.) Use the method of Lagrange multipliers to minimize f(x, y) = x² + y² subject to the constraint equation - 3x + g = 30 (You do NOT have to verify that it is a minimum.
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
The subject is differential equations 0<t 11. Use Table 5.1 to find Laplace transform for the fiunction fO). 0 t l), f(t) = 3 [h(t-1 )-h(t-4)]
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then usef(x.y) dx dy-f(g(u.v),h(u.v)|J(u,v)l du dv to transform the integral dy dx into an integral over G, and evaluate both integrals a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then...
Evaluate the surface integral FdS 11. F = x++ yj tz2k; s is the part of the cone z2-x2 + y2 for which l s z S 2, with n k positive. 11. F = x++ yj tz2k; s is the part of the cone z2-x2 + y2 for which l s z S 2, with n k positive.
Let U,V,W be vector spaces over field F, and let S ∈ L(U,V) andT ∈ L(V,W). (a) Show that if T ◦ S is injective, then S is injective (b) Give an example showing that if T ◦ S is injective then T need not be injective. (c) Show that if T ◦ S is surjective, then T is surjective. (d) Give an example showing that if T ◦ S is injective then S need not be surjective.
Need help asap. will rate Determine Laplace Transform of f(0) = u(t - 2)u(t – 3). [hint: L[u(t)] = 25 4* 4 21 Question 11 (10 points) -31 Determine Laplace Transform of f(t) Bu(t) for Re(s + 3) > 0