Find the work done by F over the curve in the direction of increasing t. F= 11zi + 11xj+ 11yk, r(t) = ( sin t)i + ( cos t)j + tk, 0sts2n The amount of work done is (Type an exact answer, using n as needed.)

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A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

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A: Given :- Consider F and C below : Fx,y =9xy2 i  + 9x2y j  C :  rt =t + sin12πt, t + cos12πt , 0≤t≤1…

Q: 2. Let y be the curve in R° given by t (t, 2 cos t, 2 sin t) for 0 < t< 47. Compute y? ds

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A: given,             x = 4 cos t, y = 2 sin t, 0 &lt; t &lt; 2∏

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A: Length of curve is given : L = integration (r'(t)dt) from a to b.

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A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

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A: As we know that, The expression for the length of the vector-valued curve is: L=∫abx't2+y't2+z't2dt…

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A: This question can be solved using the formula of linear approximation.

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A: The given graph is                                f(x,y)=1+sin(αx+y2)

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Q: r(t) = (cost, sin t,In (cos t)) from t = 0 to t= %3D (5) Find the length of the curve

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A: please see the next step for solution

Q: the function f Cx) = arc tanx for Ix|<d including f lx) = E Gas^ ng %3D %3D 2n+1 (23)

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A: Given  x=7cos(t)+sin(7t) y=7sin(t)+cos(7t) We need to find the slope of tangent at t=0

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Q: Find the work done by F over the curve in the direction of increasing t. F= 3zi + 3xj + 3yk, r(t) =…

A: Amount of work done is F.dr

Q: The parametric form of the tangent line to the image of f(t) = (5t², 2,t – 2) at t = -1 is L(t) =

A: Topic = Application of derivative

Q: 2. Let y be the curve in R3 given by t (t, 2 cos t, 2 sin t) for 0 <t < 47. Compute ds

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Q: The integral that represents the length of the curve 7(t) = (2/t, cos (2t3/2), sin (2t3/2)), where…

A: For any vector function r→(t)=f(t),g(t),h(t) ; a≤t≤b the length of the curve is given by…

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Q: 3) Find the exact length of the curve. y = In(cos r), 0 < x<

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Q: Find F. dř for F = 5yi – (sin y)j on the curve counterclockwise around the unit circle C starting at…

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Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . %3D

A: Explanation of the solution is given below...