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Q: 1. Find one normal vector of the tangent plane to f(x, y) = cos(x² + y²) at point P(1, 1, cos 2).
A: Please check step 2 for the solution.
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Q: Obtain the curvature of x= k (0 – sin 0); y=k(1+ cos0) in terms of '0'.
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Q: then the / r(t)dt is equal to r(t) = (-2 cos (21), 3 sin (4t), In (2t)), Select one: True where C is…
A: Please see the below picture for detailed solution.
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A: True.
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A: Solved the above problem.
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Q: 4. Verify that the two integrals in the circulation form of Green's Theorem are equal along a circle…
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Q: 2. Compute the vector line integral: -y х — 4 Le (x – 4)² + y² dx + (x – 4)2 + y² dy where C is the…
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Q: Find the work done by the force F = 4xyỉ + (2x2 - 3xy)j by pushing a particle along the line segment…
A: Step:-1 Given Force is F→ =4xy i→ +2x2 -3xy j→ Here, given that particle moves along the line…
Q: 3. Parametrize the circle of radius 5 having centre (8, –3) and hence find a tangent vector and the…
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- find the curl of U = exy ax +sin(xy)ay + cos2(xz) azFind the parametrization of two different curves from the point (2,4) to (3,9). Compute the work done of the vector field F=〈2xy,x2+2〉over the two curves found in part (a).Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and is parallel to the tangent line to y = 10 + 4x−x^(2) at x = 3.
- Write down the condition of tidal resonance in terms of a (mean ocean width), lambda, and n; where n is an integer equal to 1, 2, 3, …… Neglect the curvature of the Earth’s surfaceShow that the path given by r(t) = (cos t,cos(2t), sint) intersects the xy-plane infinitely many times, but the underlying space curve intersects the xy-plane only twice.Calculate for the axial force in kN at member DC of the frame shown in figure 2 using Cantilever Method. Enter absolute value and use 2 decimal places in your solution.
- True or False and explain1- For any two non parallel and non orthogonal vectors a and b with angle θ between them, it holds that cosθ(a.b) = sinθ(axb). 2- Ifr(t)=⟨−4cos(2t),3sin(3t),ln(2t)⟩,then the ∫r(t)dt is equal to⟨−2sin(2t),−cos(3t),tlnt−t⟩+C,where C is a vector constant of integration.Show that the intrinsic equations of a helix on a cone of revolution are : K= 1/as and torsion=1/bs where a,b are constant step by step with all detSuppose that U is a solution to the Laplace equation in the disk Ω = {r ≤ 1} andthat U(1, θ) = 5 − sin^2(θ).(i) Without finding the solution to the equation, compute the value of U at theorigin – i.e. at r = 0.(ii) Without finding the solution to the equation, determine the location of themaxima and minima of U in Ω.(Hint: sin^2(θ) =(1−cos^2(θ))/2.)
- A vector is said to be conservative when it's: curl equal to zero Laplacian equal to zero divergence equal to zero gradient to zero None of theseFind the gradient vector field for the scalar function f(x,y)=sin(2x)cos(6y). Enter the exact answer in component form. ∇(x,y)=Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical tangent line, or a singular point.