Determine ar, aN and k for the space curve r = (e' cost – e' sin t)i + ((V5)e')j + (e' cos t + e' sin t)k. - 7.

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Q: et C be the curve of the intersection of the two surfaces a² +} = z and 4x2 +y} +? =9. nd let L be…

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Q: H.W: Find Taylor or Maciaurin for the following functions: 1) f (x) = cos x at a = 1 2) f (x) = sin…

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Q: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

Q: Question 2 Find the minimum value of (x.y)=2xr+4y on the curve x^2+xy+y^2=16 Select one: а. -18 C b.…

A: Given, fx,y=2x+4yx2+xy+y2=16         let gx, ygx,y=x2+xy+y2-16

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Q: Let h be a differentiable function of x obtained from the parametric equations a = f(t), y= g(t) .…

A: if x=f(t) and y=g(t) thendydx=dydtdxdt

Q: Why does this work? If we have the curve in the xy-plane: F (x, y) = 0, then why is the implicit…

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Q: A circular disk of radius 5 meters centered at the origin has been unevenly heated. The temperature…

A: To find where the temperature on the disk is the greatest, we need to find the maximum value of the…

Q: 2. Find the equation of the tangent plane to f(x,y) = sin(x² +y) when x = 0, y = T. 3 and r - cost

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Q: Find the Frenet apparatus of the curve α(t)=(t , (t^2)/2 , (t^3)/6 )

A: Given α(t)=(t,t22,t36)

Q: Which point on the curve y = Vx – 1 + 8 is closest to the point (5, 8)? (x, V) = ( What is this…

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Q: I am having trouble understanding this review question. There is a curve defined parametrically by…

A: There is a curve defined parametrically by x=at^2 + bt and y=ct^3 + dt^2 + et . Here, a,b,c,d,e are…

Q: Find equations of the tangent plane and normal line to the surface x = 5y² + 5z² — 28 at the point…

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Q: onsider the curve described by the vector-valued function:…

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Q: a) y = x' – 9x?

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

Q: got y=x^3In(x), but it says to write it in y=mx+b form so im not sure if that's supposed to make it…

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Q: Consider the curve r(t) = (e' sin(2t), e' cos(2t), 2e*). (a) (b) (c) Find the osculating plane of…

A: Solution: The curve is r→t=etsin2t,etcos2t,2et

Q: Find k (curvature) and t (torsion) for curve C represented by F(t)=(e^t,-e^t,(2t)^1/2)

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Q: Let C be the closed curve consisting of line segments from (0,0,0) to (2,0, 2), then to (2,2, 2),…

A: ∮cF.dr=Line integral of vector point function taken along a closed curve. ∬ccurl F .n⏞ds=Surface…