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Q: Evaluate the iterated ntegral by Lonverting to polor coordinates. 2. zy dx dy 34

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Q: Consider the helix r(t) = (cos(4t), sin(4t), –2t). Compute, at t

A: Compute unit binormal and curvature at t=pi/6

Q: Evaluate COS Z -dz , where C is the circle |z – 1| = 3. (Integrate counterclockwise around C.)

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Q: Calculate the arc length of the curve r (t) = 2cos (t)i + 2sin (t) j + tk from point (2,0,0) to…

A: Given curver (t) = 2cos (t)i + 2sin (t) j + tk

Q: Find Laplace 2 2 [sin(34) + 65inh czt) ]

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Q: Evaluate the line integral C ydx + zdy - 2xdz; where C is the helix r(t) = costi+ sin tj+tk , 0 <= t…

A: To evaluate the given line integral.

Q: tind the Laplace trans form for the following 2メ f)= sinat uct) %3D +jat -jat e - e Euler idrolity…

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Q: Selve e the differentsal Equedon. y) = 1 , ylo)=2 Laplace Fransform using

A: Take Laplace to transform throughout the given ODE Ly''+25y=L10cos5t-2sin5t apply the differential…

Q: What is the curvature of r(t) = (4 sin t, 0, 4 cos t) ? %3D

A: Given that rt=4sint,0,4cost The formula for the curvature  is given by k=vt×atvt3 Now,…

Q: 6) Find the laplace T fhe tanction : tct) = Sint.u (t-TT) where ult - TT) is aunit tunction

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Q: What is the laplace trasform of f(t)= (e^-4t)cosh4t

A: Laplace transformation is the integral transformation that converts a function of real variable to a…

Q: Find the arc length traced out by the endpoint of the vector-valued function 7(t) = t cos t î + t…

A: Solved below.

Q: 10 eat sinh Cbt)

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Q: (a) Evaluate feay'ds with C being the right half of the circle + y - 16. Does it depend on…

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Q: The foilowing describes a para bolic path C: Pt) = (t, 2, 1-t?) %3D if F = (32, x + y+Z, 2x >,…

A: The given problem is to evaluate the line integral of the given vector field over the given…

Q: Use Eq. (9) to find the center of curvature to r(t) = (t 2, t 3)  at t = 1.

A: X-intercept is the point where graph of polynomial function touches/crosses x-axis, i.e y=0 . Y…

Q: a/ Find laplace tlanskrn LP) where A的ー at Be

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Q: y= e", osxs2 Curue leng th of the arc Set the întegral which gives the up

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Q: Eolre the following DE uing laplace trancfooy y" + 2y' ty = 0 when ylo)= 1

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Q: Calculate the fhollowoiug. Whect is 200 luceased by 70%? Q. Reud to tuoo decimsel pleces b $95…

A: A percentage is a number or ratio expressed as a fraction of 100. It is usually represented by the…

Q: Find all finchons Man sanisty he Mowing inihal problim dy %3D dy dx =4 ex ーメ how mam solwhin does t…

A: Given,           dydx=y2e-x    and y(0) = 12

Q: Use Green's Theorem to evaluate . ydx – xdy where C is the cirde centered at the origin

A: Given integral ∮Cydx−xdy, where C is the circle centered at the origin with radius 4 We have to find…

Q: Find the curvature. r (t) = 8ti+ 3sin tj+3 cos tk k(t) =

A: Use formula to calculate curvature Find magnitude of unit tangent vector

Q: The inverse Laplace hransform F(s) = 31 + Inci2-s)-nc19-s) is of %3D

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Q: Find the curvature r(t) =5ti + 3sin(t)j +3cos(t)k

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Q: Which of the following is an arc-length parametrization of the line segment from (2,1) to (1,3)?…

A: We will find out the required value.

Q: Ex: Fmd the lengthoftre arc af the Circle with P.R. ret)= [acest from Co,0 to asiut] o Ofa),- %3D

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Q: Let r (t) = . Calculate the curvature of r, as well as its arc length from t = 0 to t = 2n .

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Q: Which of the following represents the arc length of the vector function r(t) = (sin 2t, e, ) on the…

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Q: to find 2y dx-xdy, Use where C is the green's theorem the the eircle wi'th radivs 4 Centered at…

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Q: If a(s) is a curve parametrized by arc length, prove that a"(s) is per- pendicular to a'(s). (ii)…

A: Given the curve

Q: Write a formula for the curvature K(t) in terms of ( r' (t) and r" 0) )? And prove it?

A: The curvature Kt is given by Kt=r't×r''tr't3 Now prove this formula in the following.

Q: 3. Reparametrize the unit tangent vector T(t) using the arc length as parameter starting from t = 1.

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Q: If the electric intensity in the vacuum E = Eocosθar - Eosinθaθ is the divergence of the electric…

A: In the question it is asked to calculate the curl of electric intensity given.

Q: trans, Fnd the laplace tansfam of fit) the oct<I

A: To find the Laplace transform of the below function. ft=t/τ          0&lt;t&lt;τ1             t&gt;τ

Q: Find the Laplace flt)= 3t. - 5°cos 3t

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Q: Q: Prove the transfurm; formula's by definition of Laplace

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Q: Is it true that Arg(z) = arctan for x + 0, where x = Re(z) and y = Im (z) ?

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Q: The cable AB carries a tension of 400 N. Determine the moment about O (positive if counterclockwise,…

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Q: Calculate the laplace trans forms of the Pollowing Punction by using laplace txansform pains/…

A: (1) Given ft=10+7t. Consider                Lft=L10+7t=L10+L7t=10L1+7Lt We know that Laplace…

Q: 3 cosh 5t 4 sinh 5t

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Q: let rit)= demti+ dsintf+? Find the length of this curve from t=0 to t = 4.

A: we have to find the length of the curve

Q: 6. Find the arc length of the helix, r(t)=bcosti+bsintj+V1-b²tk from t= 0 to 27.

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Q: i the the position vecor be R(t) = CoS s(2t),e¯tsin(2t) ,0). Compute the curvature k(t). e

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Q: Compute the line integral f, x?dx + y²dy where the path C consists of the arc of the circle x? + y?…

A: Here we solve the given problem of integral.

Q: (4) (a) Find the contour integral de using the Cauchy integral formula, where C is the positively…

A: As per the policy, we are solving first question. Please repost it and specify which question is to…

Q: Compute the arc length function L = | ||r(u)||du for r(t) = (16t1/2, In(t), 32t), and a = 1. %3D %3D…

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Q: 2. Let r(t) = (t- sint,1-cost, tsint) Find the exact value of the curvature at t=0

A: In the above question we have to calculate the value of curvature at t=0 for the given vector-valued…

Q: From the Laplace table, determine F(s). 6. f(t) = sin 7t cos 2t (Hint: Use trigo identity first)

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