Suppose vector F represents a force (measured in pounds) and d represents the displacement of a particle (measured in feet). Which calculation below finds the work done by F to move a particle along d? O ||F x d|| OF+d O proją F OFx d OF d

Q: Find the domain of the vector function. (Enter your answer using interval notation.) r(t) = (In(t +…

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Q: Let f(t) = 3u(t – 2) – 2u(t – 6). Then f(5) = %3D %3D (A) 2 (B) 3 (C) 0 (D) 5 (E) 1

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

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Q: If f(z) = (iz? + 3z?)³, find f'(z), when z = 2i. %3D

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.)…

A: Given: rt=sqrt9-t2i+t2j-5tk To Find: The domain of a vector-valued function. Concept: The domain of…

Q: Find the domain of the following vector-valued function. r(t) = Vt+ 1i+ Vt-7j Select the correct…

A: Consider the given function. rt=t+1i+t-7j Put the each root of the function. t+1≥0t+1≥0t≥-1 And,…

Q: Q5) Find the length and direction (when defined) of u x v anc v x u. u = 2i - 2j - k, v =i - k u =…

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Q: Compute divF and curlF for F = -r°(y – 2)i – (2² + y^)j+()k. 422

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Q: Find the domain of the vector function. (Enter your answer using interval notation.) r(t) = (V9 -…

A: In the question it is asked to find domain of the vector function r(t)=<9-t2,e-3t,ln(t+2)>.

Q: se the function to find the image of v and the preimage of w. T(V1, V2) = (v, + V2, V1 – V2), v =…

A: Given Tv1,v2=v1+v2,v1-v2 and v=3,-2 , w=7,19 a) find image of v b) find preimage of w

Q: Let x be the r.v Such that ECx)=D2 ECx)=2a %3D [2+Qx}?) =2a3 %3D Findthe Value of a

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Q: Find a linear transformation T:

A: Consider the provided information, T11=23   and T1-1=05 Find a linear transformation T. We can put…

Q: Evaluate F.dr where F(x, y) =xry i+e*j and C is the line segment from (2, 0) to (4, 0). a) 0 b) 2 c)…

A: use parametrization of a line segment and formula for the line integral.

Q: At time t hours a company is selling items at a rate of r(1) items per hour. 10 Interpret the…

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Q: If F(x²_ye, ye-z?) = o then Prove that + XZ Z 2Z · Rx =

A: Given Fx2−y2,y2−z2=0 We have to show that yz∂z∂x+xz∂z∂y=xy The function Fx2−y2,y2−z2=0 can be…

Q: (c) Suppose that ø is differentiable. Prove the identity $Vø•n ds |(V*o+ V¢ • Vø) dA

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Q: OL. If w = f(u, v), u = cosx and v = sinx, show that: (30 Marks) %3D d?w dr v² fau + u?f- 2uvfuv -…

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Q: Q5) Let f(x, y) = Find unit vector for which Duf(2,3) = 0. %3D x+y

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Q: a cube of side and a function vector + zk calculate 57 Considering B=√xi-y B. dv V

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Q: ALet f (2) = x² + iy² where x and y are the real and imaginary parts, respectively of z and C is a…

A: Complex integration

Q: Let f(z) = x? + iy² where æ and y are the real and imaginary parts, respectively of z and C is a…

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Q: Use the inverse form of the first translation theorem to determine the power of e. 2! }= e't? %3D…

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Q: Let FE R?. Show that F = ő if and only if F · Ä = 0 for all vectors à E R². (This is a proof, be…

A: We have⇒    F→=0→⇒ F→.A→=0→.A→=0  for all vectors A→⇐ F→.A→=0    (f1i+f2j).(a1i+a2j)=0f1a1+f2a2=0…

Q: er(f) = ker(g) +f = cg_for some nonzero scalar c. %3D

A: We can see that the inverse part is trivial so we will prove for direct .

Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (7t + 3)i + tj, 0 sts1

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Q: Lst f: 5, - R be a bonuded. Fruction, aud. he (g,.. Lei f be tatsgrable when restricted, to ihe…

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Q: 5) Evaluate F dr where F(r, y) = ry i + j, , r(t) = ti+ 3t j, 1<t<4 %3D

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Q: Let f (z) =iz - 7x. Which of the following is correct ? oiu, = -7 v iu =-7v, i u = 7 v %D i u = - 7…

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Q: Find the domain of the vector function. (Enter your answer using interval notation.) r(t) = (V 36 –…

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Q: F• dr. Ic Evaluate F(x, у) %3D хуі + 8хyj C: r(t) = t?i + t²j, 0 sts1 %3D

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Q: prove that 16 x (I+x) dx 306

A: The product rule of integration states that∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx.

Q: Find the domain of the vector function. (Enter your answer using interval notation.) r(t) = (v 36 –…

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Q: solve for the following using the concepts of vector calculus:

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Q: 3 d The integral dxcan be rewritten as f f (u) du by making the substitution u = 4 2³ 4x³ + 3. o…

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Q: Write a in the form a = arT + aN N at t-0 for R(t) = t2i + %3D (t+r) + ( -r°*

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Q: は F-R m Show that u is 3. sauomphic to F

A: V is isomorphic to F3 means  There is a bijection map between V to F3 such that that bijection is…

Q: f 20f * f af If V²f(r,0) Find f(r,0) such that r dr v²S(r,0) = 0

A: Given:                          ∇2fr,θ=∂2f∂r2+2r∂f∂r+∂2f∂θ2-∂f∂θ To do:…

Q: Evaluate F. dr along the line segment C from Pto Q. F = -8 xi+5y j; P(-1,0), Q(7, 0) F. dr i

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Q: Find projy u. v = 7i-3j+ k, u = -4 j+ 3 k 60 45 j+ k 59 59 O 105 i- 59 45 15 k 59 59 9 9. +k

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Q: Find the domain of the vector function. (Enter your answer using interval notation.) r(t) = (V16 –…

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Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (7t + 2)i + tj, 0 sts1

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Q: eſt 2 du given that * f(z) dx = 12 f(4Tan¹(u)) 1+u² Evaluate

A: Hint :  This problem is application method of substitution in definite integral. If you have not…

Q: Let f (z) = real and imaginary parts, respectively of z and C is a contour consisting of the line…

A: The given problem is to find the Re[f(z2)] where z2 = 7+4i and given f(z)=x2+iy2 where x is the real…

Q: Determine Du f{8,1.3) for f(x,y) = 4x?y + 2xy in direction of v = (-1,1).

A: Suppose f is two variables function of  x and y  .Then direction derivative of f at any point in…

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: Given : r(t) =36-t2i + t2j-2tk   To Find : Domain

Q: Sketch the graph of the vector-valued function F(t) = (2t – 1)² î +(2t +2) ĵ. Draw arrows on your…

A: The vector valued functions in two dimensions can be represented as r→(t)=x(t)i^+y(t)j^.

Q: Given f(t) = u(t). v(t), where u(1) = ,u' (1) =, and v(t) = Find f'(1) = %3D (A) 15 (B) 53 (C) 19…

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Q: Let f (z) = . Let C be the circle |2| = 8 in z4 the counter-clockwise direction. What is 1 |f(2) dz?…

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Q: If f(2) = sin(z?) = U(x, y) + iV (x, y), determine U and V. Verify that the C-R

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Q: Find the domain of the following vector-valued function. 4 r(t) = / 36 - i+ Vij+ k V9+t ..... Select…

A: Domain of vector valued function r(t) is values of t where r(t) is defined.