- A duck is flying the helical path r cos(t), y = sin(t), and z = t with t in seconds. TE emperature is given by the function T= f(r, y, 2) = 1 +y +z?. T is in degrees centigrac , and z are in meters. Use the chain rule to compute T'(2). Give units. (ans: 4°C/s)

Q: Use an appropriate form of the chain rule to find dz/de 1. z = 3x?y; a =t and y = t? 2. z = 3 cos a…

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Q: Let I = L,x? cos(x + 1) dx. The approximation of I using the two-point Gaussian quadrature %3D…

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Q: 2. Let y be the curve in R° given by t (t, 2 cos t, 2 sin t) for 0 < t< 47. Compute y? ds

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Q: dz at (и, v) — (1,1) if du Use chain rule to find || a(w² - z + 1)-), : x = 3u – v, y = u°. 2 = x…

A: According to chain rule of differentiation . According to power rule of differentiation .

Q: Find the value of dy/dx at the point defined by the given value of t. x 5 sin t, y = 5 cos t, t= O…

A: Given, x =5sint  y =5cost We have to find the value of d2ydx2 at t = 3π4

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Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x – sin ry; y = 9t t %3D SSEVS Enter…

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Q: Consider the graph of f(x, y) = excos(xy²). Find an equation of its tangent plane at (0,0, 1) and…

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Q: az and dz Use the chain rule to find as at sin(0) r = st, 0 = s9 + t° %3D as az at

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Q: dw Use an appropriate form of the chain rule to find dt 1 w = 4 cos ry – sin cz; x=÷, y = t, z= t8…

A: Given,           w = 4 cos zy - sinxz;            x = 1/t ,      y=t,        z= t⁸

Q: 3. Find the length of the curve y = In (cos x), 0 <x <

A: we have to find length of the curve

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: Given: vector-valued function R(t) = (3 cos 2t, 9t, -3 sin 2t) Reparametrize R using the directed…

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Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

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Q: Given: vector-valued function Ř(t) = (3 cos 2t, 9t, −3 sin 2t) 1. Reparametrize R using the directed…

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Q: Use the appropriate form of the chain rule to find the derivatives. w = 3x? + 3y2 + z²; x = p sin o…

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Q: Find the speed of the cycloid c(t) = (4t −4 sin t, 4−4 cos t) at points where the tangent line is…

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Q: A particle moves in the xy-plane in such a way that its path is defined by x = e^t cos t and y = e^t…

A: Given that, x = e^t cos t y = e^t sin 2t Differentiating x with respect to t we get, dx/dt = e^t cos…

Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: Use the Chain Rule to find dz / dt or dw/ dt.(odd) z=e^r cos(theta), r=st, theta=squart of (s^2+t^2)

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Q: 3. Given that the acceleration function of an object moving along a line is a(t) = 3 cos(t)-2 sin(t)…

A: Proceed as shown

Q: as and dw/t using the appropriate Chain Function Values W = sin(4x + 5y) X = s + t, y = s – t %3D TC…

A: Given  w=sin4x+5y   x=s+t       y=s-t

Q: Find ow/@s and ôw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) x S+ t, y =…

A: Given that function w=sin2x+3yx=s+t , y=s-tvalue s=0 ,t=π2To find :∂w∂s,∂w∂tSolution…

Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t) j + 4ln(cos(t)) k,  0 ≤ t ≤ ?/4

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Q: dw at t= dt For the functions w = - 4x + 10y, x= cos t, and y = sin t, express as a function of t,…

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Q: Consider the curve where a =0 (a) Compute(t) at t = [0, +∞). (b) Find the tangent line at the point…

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Q: Use the Chain Rule to find dw/dt. w = In(V? + ° + z2 x = 3 sin(t), y = 2 cos(t), z = 5 tan(t) dw dt

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Q: Use the Chain Rule to find ôz/as and az/ðt. z = x°y5, x = s cos t, y = s sin t az as az at

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Q: 1. Find the length of the curve r(t) = (sin 2t, cos! cos 2t) from t =0 to t 2n. %3D II

A: 1)- Given: r→t=sin 2t, cos 2t from t=0 to t=2π. The objective is to determine the length of the…

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: 1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t 0 to t= 2n. CoS %3D

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Use the appropriate form of the chain rule to find the derivatives. w = 3x? + 3y² + z²; x = p sin ø…

A: Given:   w = 3x2 + 3y2 +z2  x and y and z values is given

Q: Use the Chain Rule to find dw/dt. x = 6 sin(t), y = 2 cos(t), z = 9 tan(t)

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Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< t/4

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Q: Find the exact length of the curve. y = 2 In(cos (÷)) Tt/3 < x <T/2

A: Here given Differentiate the given function with respect to x using the chain rule of derivative

Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: Find the exact length of the curve. y = In(cos(x)), TC 0 < x<.

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Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin xz; x = y = t, z = t³ t…

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Q: dz dz (a) Write down the formula for and when z f (x, y), x = x(s, t) and = y(s, t). ds dz (b) Use…

A: The detailed solution is given in the attached Handwritten notes.

Q: dz (b) Determine the by using the Chain rule with the following information: ds 2 X = - s2 2 7 z =…

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Q: dz Use chain rule to find at (s, t) = (0, 1) if ds z = 6x + y² tan e – st, y = s² – ť. x = ebs

A: Consider a function of multivariable where and . Then according to the chain rule for…

Q: dz dz and du Use an appropriate form of the chain rule to find dv' z = =; x = 14 cos u, y = 5 sin v…

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Q: Consider the following. w = y? - x, x= cos(t), y = sin(t) dw by using the appropriate Chain Rule. dt…

A: given: w=y2-x, x=cos(t) and y=sin(t) (a) we have to find the value of dwdt by using the appropriate…

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: The function w=xycosz, x=t,y=t2,c=arccost. Then we have to find dwdt(a) by using the appropriate…

Q: 3) Find the exact length of the curve. y = In(cos r), 0 < x<

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Q: бх? + 4y, : Suppose w = Compute dwldt in two different ways: x = 5 cos(t) +7 sin(t), and y = 5…

A: NOTE-By bartleby rules, only first three question has been answered. As per given by the question,…

Q: Find the length L of the curve R(t) = 4 cos(5t) i – 4sin(5t) j + tk over the interval [3, 6]. L =…

A: Given:

Q: Find dwdt using the appropriate Chain Rule. Evaluate dwdt at the given value of t.

A: to find dwdt

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . %3D

A: Explanation of the solution is given below...