Show whether the following functions are wave functions or not. 1. У(х, t) 3D А exp(ikx) = A- exp (i(ot-ф)) 2 y(x, t) = Aexp(i(k³x³-w³t³-3kwxt(kx-wt)-ip)) Аехp(1(-kx? + ot)) 3. y(x, t) =
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- Let u(t) = 9t'i+ (² -1)j-6k and v(t)= e'i+5 ej- e k Compute the derivative of the following function. u(t) - v(t) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the vector-valued function i+ k. O B. The derivative is the scalar function Click to select and enter your answer(s) and then click Check Answer. All parts showing Clear All OK earchWhich of the following pair of functions is linearly independent? (а) еЗx, е(х-3) (b) 4, sin?x + cos?x (c) 2sin2x, sinxcosx (d) sinhx, (e* – e*)Let u(t) = 5t°i+ 2-9)j-8k and v(t) = e'i+9 e-j- e k. Compute the derivative of the following function. u(t) • v(t) Select the correct choice below and fill in the answer box(es) to complete your choice. The derivative is the vector-valued function (i+ ( i+ (k. O B. The derivative is the scalar function
- 2. [-/16.66 Points] DETAILS Find the directional derivative of the function at the given point in the direction of the vector v. х, у, 2) %3Dхуz (4, 2, 8), v = -1, –2, 2] Duf(4, 2, 8) =Let u(t) = 2t°i+ (ť - 1)j-8k. Compute the derivative of the following function. (1" +71) u(1) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function O B. The derivative is the vector-valued function ()i+ (Dj+ ( k. Click to select and enter your answer(s) and then click Check Answer. Clear All All parts showingLet u(t) = 2t'i+ (P -7)j-8k and v(t) = e'i+3 ej- ek. Compute the derivative of the following function. 3t L u(t) • v(t) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function 訓 這 O B. The derivative is the vector-valued function (i+ (Dj+ ( k.
- Find (u+v).(2u-v) given that u.u=4, u.v=-5 and v.v=10Determine if u and v are orthogonal u=(cosθ,sinθ,-1); v=(sinθ,-cosθ,0)2. Find the directional derivative of 9 = yx? +x?z + 3xyz in the direction of vector n = Î + 2ŷ -? .2 Suppose that A = 3xyz² + 2xy³jr²yzk and = 3x² - yz. Find, at the point ¢ (1, −1, 1), 2.1 Vo, 2.2 V. A, 2.3 A. Vo, 2.4 V · (6Ã), 2.5 V. (Vo), 2.6 Directional derivative of in the direction of A, (0) 2.7 V × Ā, 2.8 (Vo) x A, 2.9 V X (A).
- Find the derivative of the vector functionr(t)=ta×(b+tc), wherea=⟨3,−2,−3⟩, b=⟨1,3,−2⟩, and c=⟨−2,−4,−4⟩.r′(t)=⟨ , , ⟩= Calculate the directional derivative of g(x, y, z) z² - xy + 3y² in the direction v = (1, -6,4) at the point P = (2, 1, −3). Remember to use a unit vector in directional derivative computation. (Use symbolic notation and fractions where needed.) Dvg(2, 1, -3) =A bee with a velocity vector r' (t) starts out at (7, -3, 7) at t = 0 and flies around for 6 seconds. Where is the bee located at time t = 6 if [°r' (Use symbolic notation and fractions where needed.) r' (u) du = 0 location: