Which option gives the correct parametric representation of this path?  A. x(t) = sin (2(pi)t), y(t) = cos (2(pi)t), 0 ≤ t ≤ 2 B. x(t) = sin ((pi)t), y(t) = cos ((pi)t), 0 ≤ t ≤ 2 C. x(t) = sin ((pi)t), y(t) = cos ((pi)t), 0 ≤ t ≤ 1 D. x(t) = sin (2(pi)t), y(t) = cos (2(pi)t), 0 ≤ t ≤ 1

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: 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: Find parametric equations for the tangent line to the curve x=cos⁡(t), y=sin(⁡t), z=t at the point…

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Q: Consider the curve x = et-5 cos t, y = et-5 sin t, 0 <t < 2n. a) Find the values of t where the line…

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Q: 4 TA 2 -6 -4 -2 2/ 4 6. -2 -4

A: We can find the coordinate of the image of B as below.

Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

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Q: Plot the curve c(t) = (cos t, esin t ) for 0 ≤ t ≤ 2π

A: The plot of the curve for t within 0 to 2pi is shown in figure below.

Q: 2. For the parametric curve defined by: x(t) = t2 + 4t + 2 y(t) = t³ + 2t2 + 4t + 1 (a) determine…

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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: 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: Select all parametric equations below, whose graph is the top part of the circle of radius 1. 0x =…

A: x=cos(t),y=sin(t) for t∈-π,0 This represents the half circle in the lower part. This is NOT the…

Q: Without using a graphing utility, show that the parametric curve r(t) = (3t cos(3t), 3t sin(3t), 3t)…

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Q: Generate a 3D plot based on the equation z=sin(x) +cos(y), both x and y range from 0 to 2 pi. Please…

A: [x,y]=meshgrid(0:2*pi); z=sin(x)+cos(y); surf(x,y,z)

Q: Find the equation of the osculating plane of the curve (a sin u + b cos 4, a cos u + b sin u, c sin…

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Q: Find the length of the curve traced out by the path c(t) Answer= = (cos(3t), sin(3t), 6t) for 0 ≤ t…

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Q: Q4) Answer true or false for the followings: i. if z = arc sin(xy) then z, = y/cos (z). ii. the…

A: We have to check whether the followings are true...

Q: Which is a parametric equation for the curve 25 = (x +7) + (y+ A. c(t) = (5 cos(t) – 5, 5 sin(t) –…

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Q: 1) Let 7(t) = (t, 2 cos t, 2 sin t), -4 <t< 4. Find the length of the curve.

A: In

Q: Suppose z = f(x, y) = (x² + 2) sin(y) + xy². By setting one variable equal to a constant (either x =…

A: Given surface is,This equation represents a surface in three-dimensional space.To find the:

Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

Q: express the parametric curve in the form y = f (x) c(t) = (4t − 3, 10 − t)

A: