Consider the wave equation on an infinite line, with u(x, 0) = f (x) defined by f (x) = { 0, for x < 0, x^2, for 0 ≤x ≤1, (2 −x), for 1 ≤x ≤2, 0, for x > 2. Set ∂u/∂t(x, 0) = g(x) = 0 and c = 1/2. Draw the solution at t = 0 and t = 5. Find t, at which u(15, t) = 1/2 using the D'Alambert

Q: In words, describe the curve r(t) = (2 sint,e',2 cost) for 0<= t <=6 . Be sure to a -- give enough…

A: To Explain: The parametric curve is r(t)=(2sint,et,2cost) for 0≤t≤6π , so that its graph can be…

Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: . (Section 14.4) Let curve C be described by vector function(t) = (cost-1, sint, 3/2) on 0 ≤ t ≤ b.…

A: The curve C is defined by the function,on the interval,The length of the curve on the given interval…

Q: For an equation x" +x = 0 a) Draw a tangent vector to a solution (x(1), x' (1)) in the phase plane…

A: (a) Solve the differential equation as follows: Let p=dxdt, or, x'. Differentiate it with respect to…

Q: 2. Determine the directional derivative of o(x, y, z) = re" + y² + xyz at the point (2, 0, 3) in the…

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Q: Verify that fy = fx ху ух f (x, y) = 2x'y' -x'y b. f(x,y)=(x' + y²)° а.

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Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

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Q: f (x, y) is a differentiable function with Vf(4,3) = 7i+ 5j. 2. Suppose w = (a) Find the directional…

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Q: The following r(t) = (3 sint, 4 cost) represents vector-valued function. i) ii) iii) By eliminating…

A: The followingr(t)=(3sint,4 lcost) represents vector-valued function.i) By eliminating parameter 1,…

Q: Find the tangential and normal components.  r(t)=(t+1)i+2tj+t^ 2 × k     ,   t = 1

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Evaluate I= √ (sinx+2y) dx + (6x+y)dy for the non closed path ABCD in the figure.

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Q: Sketch the direction field of the DE y'=2x+y.  (Plot 9 or more points) Then sketch approximate…

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Q: 6. Given f(x, y) = 2x³y=x²y³, a) find the directional derivative of f(x, y) at (1, 1) in the…

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Q: ex 3-4e2x 21) f dx

A: Given expression:  ∫ex3-4e2xdx

Q: F(x.y)= (v; (ス)x(0,0) f(x,y). ; (x.v) 0; (x.y) - (0,0) Given the funclion aboue, fuid the…

A: Consider a function fx,y. The directional derivative of the function in the direction of a unit…

Q: determine wave direction in the function f(x,y) x^y — x²y³ decreases faster at the point (2,-3)

A: Wave direction in the function f(x,y)= x4y-x2y3 that decreases faster at the point (2,-3) is…

Q: 10. Given the curve C defined by the vector-valued function r(t) = a) find an equation of the line…

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Q: 6. Let F(x, y, z)=2xy² + 2yz² + 2x²z. a. Determine the maximum directional derivative of F at the…

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Q: Q5) Solve the wave equation for vibration of organ pipe subject to the boundary condition:

A: In this question, we solve the wave equation by using the method of separation of variables.

Q: 18.) Compute the directional derivative of f in the given ✓ given points P. 3 a) f(x, y, z) = xy² +…

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Q: For the vector-valued function r(t) = (cos 2t, sin -(cos 2t, sin-4) 3 (4) what is the magnitude of…

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: Find the general solution to the following 3-by-3 linear system: 1 -5 10 2 -4 8 X. dt 3 -5 8.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Sketch the level curve of f(x, y) = x² — y² that passes through 5) : P = (–2, − 1) and draw the…

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Q: Find the solution of the wave equation when initial velocity equal to O and initial deflection is…

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