5) Find the arc length of the curve given by r(t) = (2.sin(t), 2.cos(t), 2 t) from the point (0, 2, 0) to the point (0, 2, 47).

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Q: Show that the function f(x, y) x4 + y? has no limit as (x, y) approaches (0,0).

A: Note: Since we can solve at most one problem at a time, we have solved the first one. Kindly…

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Q: Find the length of the curve F(t) = (eỗ cos (‡), eỗ sin(‡), eś) for 0 ≤ t ≤ 2. Arc length =

A: To find arc length of the curve

Q: Find the arclength of the curve y = (x² − 4)² on [2,4].

A:

Q: 3 5 х3; [1,3] 3 1 (с) y = у 10 У — X3 2

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Parameterize the curve r(t) = (2+ cos 3t, 3 – sin 3t, 4t) using arc length, s, as a parameter. Use t…

A: Given the curve rt=2+cos3t, 3-sin3t, 4t---1. Differentiating, we get vt=r't=-3sin3t,…

Q: Find the arc length of the segment of the curve between the lines x-1 and x-16

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Q: Find the arc length of the curve c(t) = (cos(9t), sin(9t), 2t³/2) on the interval 0 ≤ t ≤ 1.…

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Q: For the curve r-y +2xy-y+1=0: a) Find the derivative dy/dx. b) Where do the horizontal tangent lines…

A: follow the next step

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Q: ) If y = cos2x + 2cosx for 0 < x < 2n. Find the points at which the tangent line is horizontal.

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A:

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: 3.. Compute the arc length of r(0) = 2+2sinə in exact form.

A: Solving the problem.