2y X in the direction of (1, 2). Then, Suppose f(x, y) (b) ▼ ƒ(6, π) = sin 2y (a) ▼ ƒ (x, y) = cos( 2 ) ( − 2 i + ²1 COS - X X = and u is the unit vector 1/17 (-1/2 i + 1/ /j) 2 18 (c) fu (6, π) = Du ƒ(6, π) = іл 36 + j 6
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- Find the directional derivative of g(a, b) = cos(3a + 4b) at the π point ( along the direction of the vector (-4,-3)2. Find the directional derivative of 9 = yx? +x?z + 3xyz in the direction of vector n = Î + 2ŷ -? .The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(10t – sin(10t))ỉ + 3(1 – cos(104))} Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) Find the speed of the point. s(t) =
- The motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function F(t) = 4(26t – sin(26t))i + 4(1 – cos(26t))3 Find the velocity vector of the point. ü(t) = | 4(26 – 26 cos(26t))i + 4(26 sin( 26t ))j Find the acceleration vector of the point. ä(t) = | 2704 sin(26t )i + 2704 cos( 26t)j v| Find the speed of the point. s(t) = 2704 sin(26t)i+ 2704 cos( 26t)j x syntax error. Check your variables - you might be using an incorrect one.The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(22t – sin(22t))i + 3(1 – cos(22t))} Find the velocity vector of the point. v(t) = (66 – 66 cos(22t) )i + 66 sin( 22t)jv Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = 66y cos( 22t) + sin( 22t) xDefine two vector functions (t) 9 sin(t)+7 cos(t)] + (t³ - 15) k = = (t) 7 sin(t)+9 cos(t)] + tk = . Compute (t) (t) =
- Find the velocity and acceleration vectors in terms of u, and ug- de r=a cos 20 and dt = 5t, where a is a constant (- 10at sin 20 ) u, + ( 5at cos 20 ) ue y = - a cos (20) • (4 + 5t)) u, + (5a( cos (20) – 4t sin (20)) ue a =Find the derivative of the vector functionr(t)=ta×(b+tc) wherea=⟨−4,−3,5⟩ b=⟨−1,2,5⟩ and c=⟨−3,−2,−3⟩Calculate the directional derivative of g(x, y, z) = z² - xy + 4y2 in the direction v = (1,-4, 3) at the point P = (3, 1, -9). Remember to use a unit vector in directional derivative computation. (Use symbolic notation and fractions where needed.) Dvg(3, 1,-9) =
- Find the directional derivative of the function at the given point in the direction of the vector v. (0,-). v = (-3, 4) 3 π Dur(0,3 3 f(x, y) = 3ex sin(y), =Suppose f(x, y) = sin (a) ▼ f(x, y) = = 2y X 2y cos 2y 2y 2 cos (2) (2) X - X (b) ▼ƒ(3, π) = 77, 17/0 9' and u is the unit vector in the direction of (1, 1). Then, V (c) fu (3, π) = Du ƒ(3, π) = 0The motion of a point on the circumference of a rolling wheel of radius 5 feet is described by the vector function F(t) = 5(12t - sin(12t))? +5(1 cos(12t))) Find the velocity vector of the point. (t) = 60(1- cos (12t)i + sin(12t)j) × Find the acceleration vector of the point. ä(t) = 720(sin(12t)i + cos (12t)j) ✓ Find the speed of the point. s(t) = 120 sin (6t) (Write i, j, k for 2,5, k.) Submit Question