Motion along a curve:  b) r(t) = <cos(t), sin(t), t2 >. Find v(t), a(t), aT, aN

Q: Find the unit tangent vector to the curve defined by F(t) = (4 cos(t), 4 sin(t), 3 sin²(t)) at t = 3…

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Q: Find T, N and B for the curve 7 (t) = (4 cos(5t), 4 sin(5t), 5t) at the point t = 0 Give your…

A: Given that, r→t=4 cos 5t,  4 sin5t,  5t  at the point   t=0

Q: Pr. #14) Find and sketch the domain of the function in R2. In [sin- ()] (x, y) x2+y² %3D -

A: This is the problem of multi-variable functions.

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Q: Let r(t) = (t cos t, t sin t, )t . Calculate the velocity, acceleration and speed for the given…

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Q: dt cos?(t) V5 + tan(t)

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Q: Find T', N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 4t) at the point t = 0

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Q: Let h(y) = 20 cos y – 3 sin y. Then h'(y) =

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Q: Find fy ) for (x,y) Cos (x) sincy) exy

A: Given query is to find the partial derivative of the expression with respect to y.

Q: Find L{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) =…

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Q: Find T, N and B for the curve F(t) = (5 cos(4t), 5 sin(4t), 3t) at the point t = 0 Give your answers…

A: We need to find tangent, normal, binormal vectors.

Q: graphically represent the curve described by the following functions f (t) = (sin t, 2cos t)

A: Parametric curves: Let f and g be continuous functions on an interval I. The parametric equations…

Q: F(t) = %3D a. elliptical helix |F(t) = b. conical helix %3D ]F(t) = c. line d. circular helix…

A: We will use standard parametric form of these curve to match   For circle x = a cos(t) y = a sin(t)…

Q: which one of the pairs are linearly dependent? a) O f(x)=e*, g(x)3xe b) f(t) =t and g(t) =t² c) f(t)…

A: Two functions f(x) and g(x) are linearly dependent if there exists a , b , both not equal to 0 and…

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

A: We have to find the  for the given curve.

Q: 4- Find the direction and direction from the point (1, 3) for which the values off do not change,…

A: 4)Given isfx,y=e2y arc tan3y3x at point 1,3A function  fx,y has no change in any direction that is…

Q: Consider the curve defined by r(t) = (cos(t) + t sin(t))+ (sin(t)- t cos(t))] for t > 0. (a) Compute…

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Q: Graph the Plane Curve defined by: I = 3 cos(t) - t + 5. y = sin(t). for t in [0, 37]. x Clear + Undo…

A: Plot the points for different values of t from [0,3π]. Draw the curve passing through the points.

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

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Q: dy b) Find dx Y=cot4 (sinx) XU

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Q: 1. The parametric equations for the astroid below are x = sin' (t), y =- cos (1) on 0<t < 2a. a)…

A: Given, the parametric equation for the astroid below are  First need to find the stating point on…