Work done by the force F(x,y) = (3x² +3e-7+(-4y²-3xe - acting along the curve y = x³ for 0≤x≤l is equal to: O 0.35880499018099377 O 1.1917049901809937 O 0.77030499018099374 O 0.98260499018099368 O0.5590049901809937

Q: (a, o) is not measurable.

A: to find that a,∞ is measurable or not  proceed as follows We know that every interval is measurable.…

Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

A:

Q: 21. Let f(x) = 2x, x = [0, 1]. Take P = {0, 1, 1, 1, 1, 1} and set x₁=1, x₂ = 16, x3 = 3, x4={, x3 =…

A:

Q: Exercise 2. Prove that dim(null T") = dim(null T) + dim W – dim V and dim(range T") = dim(range T),…

A: We prove dim null T*=dim null T + dim W-dim V and dim range T *=dim range T for every T L(V·W).

Q: • Given f(x, y, z) = x² In(x + y- z), find f(2,4, 5). а. 0 b. 1 с. 2 d. 3 O a. b. С. O d.

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Q: F. dr Evaluate So

A: In this question, we have to evaluate the line integral for given vector function along the given…

Q: Let X; = tB¡ B,ds. | Is (X,)r20 a F - martingale?

A: Consider the given process:        Xt=tBt-∫0tBsds

Q: 1. (J · K) v (~ J. ~ K) / :. J = K

A: There are three expression in the given logical statement. They are J.K ~J.~K J≡K We prove the two…

Q: Let u € C³, v C4, A = uv". Show that rank(A) ≤ 1.

A: This is consequence of one of the famous rank theorems. Theorem:For any two general matrices P and…

Q: Let u = (-3, 1) and v = (0,3). Compute the following: u.v= • = | | i|| 2 = −1 (u · v) • (−1ū) · v ū⋅…

A: Step 1:Step 2: Dot Product (·):The dot product measures how much two vectors are aligned with each…

Q: 12. ∇⋅F of F = (2xy2)i-(3y3z2)j at (2,1,-2). a. 4 b. 27 c. -7 d. -34

A:

Q: Find ||F||. F(x, y, z) = i + j + k

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Q: 4. Compute , 3x – V1 – x² dx.

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Q: Suppose thet the filowing Aransforuution Conneclss the (x') and (ti) codmate ک ماول se4ス?) e え(スーx)…

A: Handwriting solution given.

Q: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

Q: B) If f(x.y) x'y? +x*y , find: axdy *Əyər

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Q: If f (s Continuous then on -fex) True or felse?

A:

Q: If Sc F · dr = Sc(x + 4y?) dæ + (x²y) dy, what is F?

A: Given ∫F→dr→=∫x+4y2dx+x2ydy

Q: X=(1,0,– 1, – /2)'. Then,||X||3 = ect one: a. b. 2 C. d. V2+2/2

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Q: Let Find A = x³y 1-2xz] + 2yz k Vx(VxA).

A:

Q: =gers and

A:

Q: Let f(x.y) = In (x2y). If f,(2,1)=f,(5,a) what is the value of a? O a. -1 O b. 1 Oc. 0 Od.-2 e. 2

A: From the given problem:   fx,y=lnx2y   fx2,1=fy5,a   Now,   fx=∂f∂x=∂ ∂ xlnx2y=1x2y∂ ∂ xx2y=1x2y·…

Q: Q.IB) If w=f(u, v) where u = tan ¹2 &v=ln(x² + y²), the show that: Əw dw aw +y ax dy 2- ду x-

A:

Q: 5. Calculate the divergence of F = (7x², 9y, -52).

A:

Q: let (Riae) be aring of real numbar's andf fg Eply R. Such That f= to,,-1,22010-) F-lo-してソの (hoラ-20 )…

A:

Q: Let X=(1,0, – 1, - V2). Then, ||X||1= Select one: a. -1-V3 b. C. -/3 o d. 2+V2

A:

Q: find an antiderivative Fon of the function fox)=5sinX such that FCO)=1.

A:

Q: A₁ Let 2 + sinh (2²) - ₁₁ = 27 where w = f (x, y, z)- 1 पुर Find aw дх Jw and Iw > zw. ay dz 3/20

A:

Q: f ▼ is defined by V= d/dx i + d/dy j + d/dz k and A& functions then show that V.(A+B)= V…

A: ∇=ddxi+ddyj+ddzkA and B are differentiable function then ∇.A+B=∇.A+∇.B

Q: Let f(x,y) = In (x2y). If f,(2,1)=f,(5,a) what is the value of a? O a. -1 O b. 1 O.0 O d.-2 O e. 2

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Q: Given f(x, y) = 9xy® – 6x*y. Compute: a?f ду? ||

A:

Q: Let r = xi + yj + zk and r = |rl. If F = find div(F). (Enter your answer in terms of r and p.) p'…

A:

Q: 01. If w f(u, v), u = cosx and v = sinx, show that: d'w dx2 = v? fuu + u? frv - 2uvfur - ufu - vf,

A: Given w=f(u,v), u=cos x and v=sin xso we see that dudx=-sin x =-v   and dvdx=cos x=u.By chain rule,…

Q: Let f(x, y, z)= and c(t) = (t, 13/2, t). Compute ff ds y+z

A: The given function is fx,y,z=x+yy+z, and the curve is given by c(t)=t,23t3/2,t. To Evaluate:…