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Wave Equation In Exercises 99-102, show that the function satisfies the wave equation
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- (5) Let ß be the vector-valued function 3u ß: (-2,2) × (0, 2π) → R³, B(U₁₂ v) = { 3u² 4 B (0,7), 0₁B (0,7), 0₂B (0,7) u cos(v) VI+ u², sin(v), (a) Sketch the image of ß (i.e. plot all values ß(u, v), for (u, v) in the domain of ß). (b) On the sketch in part (a), indicate (i) the path obtained by holding v = π/2 and varying u, and (ii) the path obtained by holding u = O and varying v. (c) Compute the following quantities: (d) Draw the following tangent vectors on your sketch in part (a): X₁ = 0₁B (0₂7) B(0)¹ X₂ = 0₂ß (0,7) p(0.4)* ' cos(v) √1+u² +arrow_forwardQI-A) Fund the position, vekocity and the speed of the vector function ( r(t) ) that given bekow at t-2. r(t) = 1i-t'iarrow_forwardNew calculation pleasearrow_forward
- Vector Calculus 1) Find the directional derivatives as a shown function of f at P (1,2,3) in the direction from P to Q (4,5,2) f(x, y, z) = x³y – yz² + zarrow_forward人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT 3. Obtain the directional derivative of the given function at point P and in the direction of the vector a f(x,y,z)=x^y^(2z+1)^2 at the point P(1,1,2) in the direction of a = 3i - 3]+ 4k.arrow_forwardThe position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 2 cos ti + 2 sin tj (VZ, V2) (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) = s(t) a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point. a(#) =arrow_forward
- Can someone help me fix my errorarrow_forwardDetermine whether the complex functions given below satisfy the Cauchy-Riemann equations (have derivatives).arrow_forwardCalculate the velocity and acceleration vectors, and speed for r(t) = (cos(t), sin(3t) , sin(t)) when t Velocity: Acceleration: Speed: Usage: To enter a vector, for example (x, y, z), type ""arrow_forward
- Question described by the vector function r(t) = (4t² Int, -2e-3t). t-4 a) Find the integral ſ r(t)dt. b) Find parametric equations for the tangent line to the given curve at the point (0, -3, -2e-³). c) Consider the curve which is 29 Can you find parametric equations for the tangent line to the given curve at the point (0, -2,-2)?arrow_forwardProve that a parametric function given by I= 2t + 31 y = t² + 2t* satisfies the equation v- (2)' • •(2)' dr drarrow_forwardPlease give me answer very fast in 5 min siniarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage