Section 7.1 p. 623/625 # 2 For the following exercises, sketch the curves below by eliminating the parameter t. Give the orientation of the curve. 2. x = cos(t), y = sin(t), (0,27]

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: The function r(t) = (4 cos(t))i + (4 sin(t))j traces a circle. Determine the radius and center of…

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Q: Find the speed at the given value of t. r(t) = (sin(3t), cos(6t), cos(7t)), t = " 2. II

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Q: The equation 2– 2x + 2y - 4y = -1 is Select one: O an ellipse with center (1, 1) and foci (2, 1),…

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

Q: Q4] (15Marks) Sketch the curve r cose. %3D

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Q: How do the paths r1(t) = (cost,sin t) and r2(t) = (sin t, cost)around the unit circle differ?

A: Given :                   r1(t) = cos t , sin tr2(t) = sin t , cos t

Q: Suppose that the temperature T at point (x, y, z) is given by T(x, y, z) = sin(xyz) and that an…

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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: Question 2 Express the curve by an equation in x and y given x(t) = 11 – sin(t) and y(t) = cos(t).…

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Q: 14. Find the length of the curve C. a) C: F(t) = (cos³ (t), 3, sin³ (t)), 0≤ t ≤π/2 b) C: F(t) = (t…

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Q: Find T', N and B for the curve 7 (t) = (2 cos(2t), 2 sin(2t), 3t) at the point t = 0 Give your…

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Q: 21. For the curve 7(t) = sin ti + cos tj, find 7 '(t) and sketch the position vector 7(÷) and the…

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Q: a:1 c R E4 t a(t) = (cos (), sin (), 2, at) %3D ↑

A: Given the curve  α:I⊂ℝ→ℝ4 given by t→αt=cost2, sint2, 2, αt

Q: 1. Consider the position function 7 (t) = (4 sin(2t), 2,4 cos(2t)). (a) Sketch the path of this…

A: Curvature: The curvature of postion function r→(t) is given by, κ(t) = T'(t)r'(t) Given: r→(t) =…

Q: Find the length of the curve 7(t) = (cos(4t), sin(4t), 5t) for – 8 <t< 1 Give your answer to two…

A: use the arc length formula for finding length.

Q: Find ſo F · dr for F = 8yi – (sin y)j on the curve counterclockwise around the unit circle C…

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Q: Draw the Projections of the curve on three coordinate planes.  Use these projections to help sketch…

A: Given,        r(t)=t, sin(t), 2cos(t)

Q: Let Sketch the curve and find the length of this curve. r(t) = (t, 3 cost, 3 sin t), 0≤ t ≤ 2π.

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Q: Q2: Gruph the nector fundion Tt)= Find the equat in for the tanget f functron fexy) = SinCxy) at…

A: a) Given,  rt=cost, sint, t Here  xt=cost,yt=sint,zt=t