Consider the IBVP of the wave equation U – Uxx + U = 0, 00 u(x, 0) = 9(x), u, (x, 0) = (x), 0 < x

Q: X 1 (A) If g tan , find the derivative 1² +2 yz of g at point (1,2,-1) in the direction of the…

A: Directional derivative of the function

Q: Q4) a) Find the tangent plane and normal line of the surface f(x, y, z) = x? + y²e* + z? = 3 at…

A: Solution:

Q: If (x, y) moves from (-2, –1) towards (1, 5) for a distance 0.02, then which of the following is…

A: fx,y=exyPoints from−2,−1 towards 1,5 for a distance 0.02

Q: The equations ry? + 5zzcos(u) + ye" = 10 and zyz + ze" - 4u = 12 are solved for u and v as functions…

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Q: The equations ry? + 8zzcos(u) + ye" = 16 and r*yz + xe" – 5u²v² = 15 are solved for u and v as…

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Q: 4. Compute the first fundamental form.

A: Given xu,v=u2-cosv,u+sint, cosv

Q: The maximum directional derivative of f(z,y,2) sin(zy)-ya +10 at (-1, 2, 0) is Question 5

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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: Find the directional derivative of Du" f (2,1) in the direction of: a = 3i + 4j To f(x, y) = InGes…

A: Gradient of a function :  Let f be a differentiable function at  x , y  and let f x , y  have…

Q: 2. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment…

A: We will solve both the parts using the basics of integral calculus, in particular double integral,…

Q: 18 The equation 10 14 - 2 = 0 defines z as a function of x and y. Find dz/dx and dzldy at the point…

A: 18x+10y+14z-2=0∂∂x18x+10y+14z-2=∂∂x(0) [Differentiate both sides with respect to…

Q: a²u อใน 0²4 - 0x² = ²x cost e2x at (00) u(0,t) = 0, u(ñ, t) = 0, u(x, 0) = 0, u(x,0) = 0 at

A: Introduction: To determine initial boundary value problem, Laplace transformation is very important.…

Q: Study the analytically of w = L_r(z) at the points z = 0, z = v2,z = -2i

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Q: 1. y = 2t2 – 7t3, x = 9t – t5

A: dy/dx and d2y/dx2  are find in next step dy/dx = (dy/dt) /(dx/dt)

Q: Let f(x, y, z) = x“y + z* and x = s³, y = st°, and z = s°t. (a) Calculate the primary derivatives ,…

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Q: If y = f(x) defined as parametrized r(t) = 4t- 2t2, y(t) = 3t - t, then which of the following is…

A: Hee, given that y=f(x) defined as a parameterized x(t)=4t-2t2;y(t)=3t-t3 So, y'=dydx=dydtdxdt…

Q: Example Let f(r,y, z) = ryz sin rz. Find Vfo at the point Po = (1, –2, 7) and compute the…

A: to find : (1) grad f. (2) directional derivative.

Q: 2. Solve V'u = 0 for r<1, 0<z< T, u(r, 0, 0) = 0, a7(r, 0, 7) = 0, - u(1, 0, z) = z cos³ 0.

A: It is given that

Q: Using Bernoulli's equation, solve for the general solution of dy +y = 2xy²e*. Please show complete…

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Q: Find the directional derivative of f(x, y, z) = ((x+y+z)e², (x² + y²)e-²) at c = (1, 0, 1) in the…

A: The given problem is to find the directional derivative of the given vector function at point…

Q: g) The integral S tan(vx) dx x cos2 (Vx)

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

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Q: Calculate Vf, V•f, V×f f (x,y. =)= xi+ y'j-* by the function

A: Introduction: The curl of the vector f(x,y,z)=fxi+fyj+fzk is given by ∇×f=∂∂xi+∂∂yj+∂∂zk×fxi+fyj+fzk…

Q: Consider the family of functions uc(x,t) of two variables x,t, indexed by the parameter c,…

A: Given partial differential equation or wave equation is 13∂2u∂x2 -8 ∂2u∂t2=0 -----(1) Also, given…

Q: 5. Compute the lenght of the curve u = t, v=0 from t = 0 to t = 1 using the first fundamental form.

A: Suppose, a continuous function is provided over a certain interval. The arc length is the length…

Q: Consider the differential equation y' = 2y X a) Sketch the slope-field for x in [−2, 2] and y in [0,…

A: Given: Differential equation y'=2yx. To do : a) Sketch the slope-field for x in [-2, 2 ] and y in…

Q: = (u² - cos v, u + sint, cos v) x(u, v):

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Q: Example: Sketch the direction field for equation: y' = y(2 – y). (1) Evaluate slopes at several y's.…

A: Slopes of y's yy'=y(2-y)y=3-3y=20y=11y=00

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: Solve  using wave equation: u(0, t) = u(π, t) = u(x, 0) = 0, du/dt | t = 0 = sin(x)

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Q: 5. For each of the statements given below decide if it is true or false. If it is true explain why.…

A: We check that given statement is true or false.

Q: Find the derivative, dy/dx of the following using the chain rule: a) y = 3. 'x+1 b) y = ()³ 5x+1 %3D…

A: As per guidelines we can solve only one question at a time so if you need more answers kindly repost…