dv a) V5v + 4 b) V² – 4 dt |PVP+I dt

Q: f(æ, y, z) = æ²y+ 2y²z+ 3æz?. Compute fa: (1, 1, 1). None of these. 3

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Q: Evaluate the line integral. | (9x – 9y) ds C C : x² + y² = 64 | (9x – 9y) ds = C

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

Q: ▪1 2 6t5 dt du %3D 1 + t6 u | 2 %3D 1 II

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Q: こ= (t)} () て= () %3D - (^),J %3D てんn ZトXC

A: →∫eax+bdx = eax+ba + C, where 'C' is the constant of integration.→∫xndx = xn+1n+1 + C

Q: Determine the Linearity of this DE. * ay dy ニ X Linear O Non-Linear

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Q: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

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Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

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Q: Solve Utt (1,4) Ux (o,t) =o UCX, 0) = 0 KUXX (xst) 0Lxo %3D Ux (1,t) = 0 Ut (x,0)= 2 %3D -1 %3D…

A: The given problem is to find the solution for the given wave equation partial differential equation…

Q: Use the method of separation of variables to solve: (ôu ôu - = 0 in (0,1) × (0,+∞), (2) u(0,t) =…

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Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y+ z + w= 6 .…

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Q: If W = 2x3 + 3y², a 5t2, y = 2t³ %3D = %3D dW then find at t= 1 dt O 1912 O None O 1273 O 1572 2212

A: A detailed solution is given below

Q: 2. What is the relation between dV /dt and dr/dt if V = ()7r? %3D

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Q: d [u (v X w)] = dw. lu • (v X w)] = [v X w]+ u• xw] [v X w] +u * + u * [v X dt dt dt Idt

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Q: Compute f, aL a2f and :f(x, y) = (x + y)(2x + y)² ax' ay дхду

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Q: SLre to shoN your sclubion at the nigt column llustration Solution 1 z=1.19 2. 2-0.98 3. z0 08…

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Q: If (x, y, z) = x²yz³ and A = xzi -y²j + 2x²yk, Determine : ww a) Ax (Vx A) at point (1,-1,1) b) VX…

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Q: If V = (3x + 2z²)i + j- (z – 7x)k then V. V at the point. (1, 1, 1) is ||

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Q: If f(t)dt = r2 %3D 55

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Q: dv av and ду ди ди 2. suppose f(z) = u(x,y) + iv(x, y), show that əx %3D ду əx ||

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Q: 12. Calculate the area and volume of a sphere knowing that the length of its equator is L = 12p cm.

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Q: Utt = 8uxx for 0 < x < ™ u(x, 0) = x² u(x, 0) = 1/2cos(8x) Uz(0, t) = u„(T, t) = 0 %3D II

A: The given P.D.E is                            utt=8uxx for…

Q: 9x + 2y + 4z = 20, x + 10y + 4z 6, 2x-4y + 10z =-15 54x +y+z = 110, 2x + 15y + 6z = 72, -x + 6y +…

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Q: and v= x2y% if z- fcx,y) where show that dz dv u=X-y 出。是、会 dy 24

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Q: Use Cramer's rule to solve for y without solving for x, z, and w. 4x + y + z + = 7 5x + 3y z + 8 W…

A: Let's find.

Q: Evaluate f(х, у) ds. f(x, у) %3D у + 3 s: r(u, v) = ui + vj + 4vk, 0 sus 1, 0svs 4

A: Given: fx,y=y+3 S:ru,v=ui+vj+4vk, 0≤u≤1, 0≤v≤4 Differentiating r with respect to u, ru=1,0,0…

Q: (a) Vx E R, 3y E Z such that y > x + 110. (b) Vx E Z, 3y E N such that y > x + 110. (c) 3x E Z such…

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Q: Use Cramer's rule to solve for x, y and Z 2х + у — 3z %3D 0 | 4х + 5y + Z %3D 4 %3D

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Q: ab c Pq r U V W a. det (2B¹) where B = 4u 2a 4v 2b -q 4w 2c <-r 2p -a+u 3u b. det (20¹) where C =…

A: Given problem:-

Q: Integrate counterclockwise z + 6 dz, C: |z – 1|= 4 Z – 2 z + 6 dz 2 ||

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Q: Express In x V in terms of in x, In y, and In z. 2mx-글 my-글 nz 2 Inx + 글 Iny-글 mz znx+my+nz In y 2nx…

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Q: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

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Q: Compute the Vf = (x, y) for f(x,y) = 5y – x³y2 %3D %3D

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Q: A LTI systemis deseribed by the DeE ý+6y+8y=2x4) find hit),then find.y(t).if X(t) = te t>o. -2t %3D

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Q: linear or nonlinear.

A: A PDE is said to be linear if the dependent variable u and all its partial differential coefficients…

Q: Fx, y, z) = (10y – az – 5x)i + (3by – x + 8z)k + (z – 5y + 2cx)j %3D a

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Q: I ntegrate: Sv V v+2dv HIN T: If u =x+Q, then × = U-a

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Q: - Calculate the 2D 32×32 DFT of ƒ(r,y) = 26(r,y)+ 6(x – 15, y – 16).

A: The given function is f(x,y)=2δ(x,y)+δ(x-15,y-16) The 2D DFT signal is given by…

Q: d.x = -2x + 5Y dt dy -2.x + 4y dt 5 cost X = \ sin t et 3 cost –

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Q: Find the gereral Solution of the fille d dffferential equation. 3,n1 %3D | -

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Q: 4. and A= Find flA) where f lt) = t"-2t+3t+ 3t +2 て %3D %3D て

A: Given,  A=124-1 f(t)=t4-2t3+3t2+3t+2 Find: f(A)

Q: Solve for z using cramer's rule.  2x-y-z=4 4x+y+z=2 3y+z=2

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Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: differentiate. a) g(t)こ3-2t St +1 c) H(u)= (u-JJ) (utro) d) FLt)- モ-3 %3D

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Q: Evaluate [ ( (x2+ yz) dV, where R is the rectangular box 0 s x < 1,1 s y s 2,1 s z s2.

A: follow next step

Q: me succe LO SUIVE uie folnoWing 2 и (х)— | (x -t )u (t )dt 2 --

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Q: (b) Compute f er+uds, where c(t) = (t, 2t), t e [1, 2]. %3D

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Q: (b) xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z < 0}.

A: We have to evaluate given integral:

Q: 4. Show that 4= 3y'z' i+4x²:* j+6x°y°k is solenoidal.

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Q: If dr/dt= -r5, what is r(t)?

A: Given drdt=-r5. The we have to find r(t) = ?