Consider the helix r(t) = (cos(-4t), sin(-4t), 3t). Compute, at t = :

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…

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: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

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Q: Let C' be the circle |2| = 3 in positive sense. Find ( sin(r2*) + cos(72²) dz cos(T2²) (2 – 1)(2 +…

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Q: [ sec2t dt + S sin?t dt + § n'-1dt

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Q: Suppose C is the curve given by r(t) = (3 cos(t), -3 sin(t), 4t). Find an equation for the…

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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 F-dX where C is the curve X(r) = r°I+( 2r+ 1J, 0<I55, and Fxy) = rI+yJ.

A: 9

Q: Find f (x-y3)d a + xy dy if the contour C looks as follows: It consists of two arcs of radius 1 and…

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Q: Sketch the two curves 7(t) = tî + t²j; t e [1, 5] and B(T) = e"î + e²r3; T E [0, In 5]. How are they…

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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: 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: 4) Evaluate (¹ + tany)dx + xsec²ydy where C is the curve Y=X²-1 from (1,0) to (2, 3)

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Q: Find the length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:

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

A: In

Q: A glider is soaring upward along the helix r(t) = (cos t)i + (sin t)j + tk. How long is the glider’s…

A: Given: The path of glider as r→t=cost i^+sint j^+t k^, To find: The length of the glider's path from…

Q: Find the length of arc from (2,1) to (4,4) of the curve x = 2√y

A: Let us consider curve x=g(y). The arc length of graph of g(y) from point (a, f(a)) and b,f(b) Arc…

Q: 11. Find T(t), N(t), B(t) and x(t) for the circular helix: r(t) = (sin5t,- cos5t,12t)

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Q: 11) Draw the curve F(t) = ß cos(1) 7+ y sin(t)] + tk. Label some key reference points, and indicate…

A: The given parametric curve, r¯t=7 costi⇀+3sintj⇀+tk⇀. To Sketch: The curve and label its points and…

Q: Find T, N, and K for the plane curve r(t) = (4cost + 4t sin t)i + (4sin t-4t cost)j, t> 0.

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Q: Use the chain rule to find az as az at = Z= sin (0) az as az at r=st, 8 = 5³ + t² and

A: The objective of this question is to find the derivative of z with respect to t using the chain…

Q: Let C be the curve defined by r(t) = (2 cos t,t,3 sin t), where 0<t< 2t, (a) Use a table of values…

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