Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. r(t) = (3 sin(t), 4 cos(t)) y 2 1- 1 0000 1 2 3 4 5 -4 -2 -1 -1- -2 0 - 4 -3 -2 -1 3 2 1 -1- -2 -3 1 2 4 -5-4-3-2-1 2 -1 -2 3 -3 1 2 4 -5-4-3 -2 -1 2 1 -1 -2 1 2 3 5 X

Q: (9.) r(t) = (1, cos t, 2 sin t)

A: As per your query the solution of question no 9 is given the next step.

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A: It is a basic questions of 3-D geometry , we have equate the equation only

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A: The direction derivative  of f(x,y) in the direction of unit vector, is defined as follows.

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A: We have given the function;

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A:

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A: we now that if velocity vectoe at time t is  v(t)=vx , vywhere v1  and  v2  are integrable function…

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Q: e vector equation ū=

A:

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A: Here, a'(t)=(1,2t,2t)a'(1)=(1,2,2)anda(1)=(2,1,3)

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A:

Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A:

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A:

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Q: 3. Turn in: Find the equation for the tangent line to the curve defined by the vector-valued…

A: We have to find the tangent line For this we doing derivative.The procedure is given below

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