Let A=[ Let B=A -t| 3. -2 where t is scalar, Fao which velve (s) of t is B singular?

Q: Let r be a differentiable vector function of t. Show that if r . (dr/dt) = 0 for all t, then | r |…

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Q: Consider the vector field F = F . dī along the curve C: F(t) = 7 cos(t)i + 7 sin(t)3, 0 <t <…

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Q: Exercise 2. * Let f(z) Fa- and C: Iz – 9| = 1. Then f. f(z)dz = sin(32) a. 0 b. 2ni c. 9 d. None of…

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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: Show that F is a conservative vector field and use this fact to evaluate F. dr along the given curve…

A: Consider the given function. Fx,y=x2i+y2j The compare the form of the function with the general…

Q: Show that the vector function r defined by r(t) = ƒ(t)i + g(t)j + h(t)k is continuous at t = t0 if…

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Q: Let r(t) be a differentiable vector function such that r(t) · r '(t) = 0 for every value of t. Prove…

A: Given that the data, r · drdt = 0  .....(1)

Q: 3. Let F = (2y? + z)i+ 4ryj + rk. (b) Using the fundamental theorem of calculus for line integrals,…

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Q: Consider the vector field F = (5x + 6y, 6x + 4y). F - dr along the curve C given by r (t) = (t², t*)…

A: ∫CF→·dr→=∫abF(r(t)) r'(t) dr

Q: Find an expression for the vector field F = ⟨x - y, y - x⟩ (in terms of t) along the unit circle…

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Q: State whether the following derivatives of vector-valued functions rị(1) and r2(1) are scalars or…

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Q: Let F (4t +3, sin(3t), 42) Find the indefinite vector integral | F(t) dt = ( +C1, +C2, +C3)

A: Given,F=4t+3,  sin(3t),  4t2∫F(t)dt=?

Q: Find the domain of the vector functions, r(t), listed below. using interval notation. 1 a) r(t) = (…

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Q: 41. Let r be a differentiable vector function of t. Show that if r•(dr/dt) = 0 for all t, then |r|…

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Q: 5. Let F(r, y) = ye²vi+ (xe"V – 1)j. (a) Show that F is a conservative vector field. (b) Find a…

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Q: For the scalar function f, div(grad f) is equal to Select one: а. a²f -k dz? i+ dx? b. Non of them…

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Q: 9. Sketch the vector field F(x, y) : :(yi — х). Vx? + y?

A: Consider the given filed, Fx,y=1x2+y2yi−xj Further simplify. Fx,y=yx2+y2i-xx2+y2i=〈yx2+y2,-xx2+y2〉

Q: Let r(t)= Determine the interval(s) on which this vector valued function is continuous.

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Q: Consider the scalar field f(x,y, z) = 2x² – y² + 3z? Determine V Vfl(1.-1.1) II. VxVfl1.-1.1)

A: Here, the given function is: f(x,y,z)=2x2-y2+3z2

Q: Let F = (4t + 2, sin(2t), 4r“) Find the indefinite vector integral F(t) dt = ( |) + (c,,C2, Cs)…

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Q: Sketch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line…

A: The solution are next step

Q: Question attached thanks!

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Q: 2. Consider the vector valued funcion In(1 – t) /t+I, e-1/lt| if t +0 R(t) = t (1,0, –1) if t = 0.…

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Q: Determine the vector field of F. F(x, y) = 8i – 4j 1 1

A: We have given vector F=8i-4j. We have find the vector field.

Q: Sketch the vector field F(x, y) = i- 5jand calculate the line integral of F along the line segment…

A: Let's find.

Q: Sketch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line…

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Q: Find a non-zero and non-constant vector function F(x, y) = F(x, y)i+ F2(x, y)j, %3D OF OF F such…

A: Given, to find a non-zero and non-constant vector function in the form…

Q: Find the flux of the vector field F = through the half-sphere z = V1 - x² - y2. none of these above…

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Q: Consider the function f (z) = e2? (a) Use the Cauchy-Riemann equations to show that f (z) is not…

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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: dr = wa x b dt r X

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Q: Find the net outward flux of F =axr across any smooth closed surface in R, where a is a constant…

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Q: Compute the integral of ſA° · dľ°P2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function…

A: We have to find the integral from point p1 TP p2.

Q: Find the values of real numbers a, b, and c such that the vector-valued function - {(at?, a(t + 1),…

A: A function f is continuous at x=a if

Q: 1) Sketch the vector field F. (i) F(r, y) = (ii) F(r,y, 2) = i

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Q: ) Show that the vector field, F3 yz £ + zx ŷ + xy 2 c

A: Given: The vector field is, F3 = yz x^ + zx y^ + xy z^

Q: (10) Given that the vector field F= 2z i- 3 x j + 4 y k Evaluate f F. dr where S is the portion of…

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Q: Let R be a vector-valued function defined by VA -1, , In(t + 1) sin 3t if t+0 (2, 3, 0) if t= 0.…

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Q: Let G = e'i + 4t³ cos (t + 1) j+ te" k Find the indefinite vector integral G(t) dt i+ j+ k+C where C…

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Q: The figure shows a vector field F and two curves C_1 and C_2. Are the line integrals of F over C_1…

A: The figure shows a vector field F and two curves C_1 and C_2. Are the line integrals of F over C_1…

Q: 6. Determine whether or not the vector field F is conservative. If so, ind a potential function f.…

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Q: Consider the vector field F and the curve C below. F(x, y) = x2y³i + x³y?j, C: r(t) = (t2 – 2t, t2 +…

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Q: Let r be a di¡erentiable vector function of t. Show that if r # (dr/dt) = 0 for all t, then  r  is…

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Q: Determine the vector field of F. F(x, y) = yl – xj 1.

A: Solution

Q: Let F = (t+ 4, sin(4t) , t°) Find the indefinite vector integral F(t) dt = ( +C1, +C2, +C3)

A: Given, F = (t+4, sin (4t), t³) ∫F(t) dt = ∫(t+4, sin (4t), t³) dt ∫F(t) dt =( ∫(t+4)dt , ∫sin(4t)dt…

Q: (d) Let y and be scalar fields. Prove that V (Vy x V) = 0. (e) R=xi + yj + zk and let r = Prove that…

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Q: Consider the vector Field 7 and the curve C below. F(x,y) = (3 +4 ху?) 1 + 4x²yј, C is the arc of…

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