3. If laplace f(t) = find laplace f(4t)

Q: Prove or disprove that if ∇ . F = 0 and ∇ * F = 0, then F = 0

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Q: Eliminate the paranoter t from the follewing S r(1) = 4+ sin t lu(t) 3- cost

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Q: 3. Consider the parameteric equations for a curve C given by x(t) = cos t(1 – cost), y(t) = sin t(1…

A: Given that: xt=cost1−costyt=sint1−cost

Q: Find T, N and B for the curve 7(t) = (4 cos(2t), 4 sin(2t), 2t) at the point t = 0 %3D Give your…

A: given that                                          r→(t)=4cos(2t), 4sin(2t), 2t at t=0…

Q: - 3 sin( – 5t)). Let r(t) = (2t³ + 4, − 5e¯ - Find f(t)dt (don't include the +C) fr(t)dt = { "

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 2. § F•dï , where F = (ycos(x) – xy sin(x), xy + xcos(x)) and C is the C triangle from (0,0) to…

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Q: Find the length of the curve given by ř () = (6t, 12/T, 3Int) for 1<tse. O 8e-4 O 2e-1 O 4e - 2 O…

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Q: The curvature of a function y = f(x) is given by the expression y" (1 + (y')²)³/2 Determine a…

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Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

Q: if y= Cot" (-+) y=Cot Prove that dy 1-x

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Q: ) For the following function, determine whether u and v are harmonic (satisfy Laplace equations) or…

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Q: find the Laplace invers L 2 s(s+2)

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Q: Find the unit tangent vector to the curve defined by r(t) = (5t, - 5t, √1-t²) at t = 0.

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Q: Problem 1) For a vector-valued function with a parameter called u, ř(u) = , find a real-valued…

A: s(t) = √34 t

Q: A. From the Laplace table, determine F(s). 5. f(t) = (3t + 1)50

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Q: Find 00 et (ii) L-1 [cot"" ())

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Q: Use function f(x)=x-Cos(x) to differentiate Newton,s. Method and Fixed point method.

A: Given that f(x) = x - cos(x) ---(1)   To get the solution of f(x)= 0 we first apply fixed point…

Q: The orthogonal trajectories of the family of curves r = c(cosec 0 + cot ) are given by: (a) ke-cos e…

A: See this solution in below

Q: A. From the Laplace table, determine F(s). 2. f(t) = (t + 1)50

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Q: Find (cost using Laplace find [[ sint] using Laplace

A: Here we can use following formula of Laplace transform 1. Lcosat=ss2+a22. Lsinat=as2+a23. Lftt=∫s∞Fs…

Q: 3. (a) Find an equation for the tangent line to the curve parameterized by 3(t) = (. e"-) at the…

A: Given data: s→(t)=t3+t+2t2+1, et2-1 point p→=&lt;0,1&gt; So, x=0, y=1⇒t3+t+2t2+1=0et2-1=1=e0…

Q: - 3t 3t 2e-³t). Let r(t) = (2t — 4, 5e¯ Find the line (L) tangent to r(t) at t = = 1.

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Q: 1. Find the unit tangent vector to r(t) = at t = n.

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Q: Find the equation of the tangent plane to z = In(x²y) – x/ỹ at (-,4).

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