Evaluate the line integral SF. dr for the vector field F = x√yi+yz²j + sin(z)k along the curve given by r(t) = t² i + t²j+t³ k, 1 ≤ t ≤2. ScF-dr= =

Q: (3) Evaluate the integral F. dr where the vector F is defined by F = and where the curve C is…

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Q: Draw the slope field (direction field) for the following DE: y'=y-t

A: Given DE is Make table as follows:…

Q: OSketch the vector field F(x, y) = -5i – 5j and calculate the line integral of F along the line…

A: Solution:-     Given that, F→ x,y=-5i∧-5j∧we have to calculate the line integral ∴we have to…

Q: Calculate the divergence of the vector field F (x, y, z) = − 10 sin(2xy)i — cos(x³y)j. (Give an…

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Q: Find the work done by the vector field f = to move a particle along the arc of the hyperbola y=1/x…

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Q: Use the fact that \bF = (2xy + 3cosy) bi + (r? - 3xsiny) bj, is a gradient vector field to evaluate…

A: Given F = (2xy+3cosy)i+(x2-3x siny)j As F is a gradient vector field, it can be rewritten as F=∇f…

Q: A vector field F = x(x² – y²) + ŷ(2xy + y?) a) f d.č =? c on the closed curve in the figure b)…

A: a) Consider the figure:

Q: As the number of hours since you ate protein increases from 2 to 2.75 hours what is the average rate…

A: Given: At 2 hours B1=1100 mg/L At 2.75 hours B2=1025 mg/L

Q: Let r = (x2 + y?)/2 and consider the vector field F = r4(-yi + xj), where r 0 and A is a constant. F…

A: Given,r=x2+y21/2;  F→=rA-yi→+xj→ ;  r≠0; A is a constant. (a). To find, curlrA-yi→+xj→. curl…

Q: Verify if the vector field F = (x° cos(4y), -x sin(4y)) is conservative and evaluate the line…

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Q: Consider the line integral cos(x+2y)dx+2cos(x+2y)dy where S is a curve starting at (0,0) and ending…

A: We have to show that F is conservative. When F is given as F=cosx+2yi+2cosx+2yj For the conservative…

Q: Consider the functions below. F(x, y, z) = xizj+yk r(t) = 4ti + 6t j - t² k (a) Evaluate the line…

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Q: .) Find the work done by field F = (-y,-x) along curve C: counter clockwise along semicircle y = v4…

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Q: da potential function for the vector field F(x,y) = (16xy + 8y - 2,8x² +8x).

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Q: Anna is to create a garden plot to grow lettuce (area A) for her turtles, as well as flowers (area…

A: When the given curve y = 9 - x2 intersects the x-axis, we have                y = 9 - x2 = 0…

Q: 5. Let 7(t) =. a. Find the domain of the vector function. b. Evaluate lim1 7(t).

A: (a). r→(t)=3et-1t, t3-t2t-2, sin(πt)ln t

Q: 3. Find the line integral fF.dr where C' is the circle of radius 5 in the xz-plane oriented…

A: The given vector field is .Find the value of line integral  as follows.The parametric surface can be…

Q: Suppose f = sin(x - 2y), and the vector field F = ∇f. Find the following curves: C1, which is not…

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Q: Let be a potential for the vector field F = (-24 x³z + 6 xyz², 3 x² z² + 15y¹, −6 x¹ + 6 x²yz - 10…

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Q: I. Consider the vector-valued function In(2t + 1) Ŕ(t) = ²₁+ î+ t 1. Determine the domain of R. 2.…

A: This is a problem of Vector Calculus.

Q: Consider the vector field F = ⟨ 1 , y ⟩ .Compute the path integral of this field along the path:…

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Q: 14. A number of grade nine students were surveyed and asked the question "Do you Feel Safe at…

A: Total number of opinions in the survey=6+20+35+29=90 Category Number of opinions corresponding to…

Q: Let F = yi + xj + x³y³ z³k, C the curve x2 + y² + 6x – 2y + 9 = 0, z = 2 (with counterclockwise…

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