A campround coner has I50D m tencing. c wants to endsc a reonclar tield lbwsdhueng a ruer, wwh no herans along river, Lckx', represent ,idth bf feld Llus a) wrte an expression for length of held as hinchin tFX ) Find area of field (axw) as funchon of X cFind the value vf x leading to the mayimuna area d) Find the maximum area.

Q: gral of the field F(x,y,z) = 7xi + 7yj + 7zk across the portion of the sphere x2 +y² +z? = a? in the…

A:

Q: 1 Usng the eqressions for the volune and area in n-dunensond 2/2 Space givan by Vncr) 11 " and AnG)…

A:

Q: Evaluate the line integral S 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). So…

A:

Q: Consider a vectanial field P:D CIR° =zR3 If we Know that DxF = Ô Which of the following state menst…

A:

Q: Find the wark done by the Foree Field FoK x>ye^> along the parabola X=y+1 from (bo) to (2,1).

A:

Q: Find the wolonm of inforachom

A:

Q: Let C:z|=1 in the counterclockwise direction and I = $. Lnzdz, J = $. zdz, and K = %3D $. cotzdz.…

A: We apply Cauchy Goursat Theorem to the given questions. For complete solution kindly see below step.

Q: Find a definihen ofa duisbailiky khatin | on by ris rule : for eluments A snd B g Im, ALB if and…

A: It is given that

Q: dy Find the slope field of dr 2x using GeoGebra.

A: The slope field is very significant in the ordinary differential equation. It helps us to understand…

Q: E valugte the cube raot of z when 2=27 Cis(210) ( Let 0s GS360°) Smallost ☺ ualus) targonst ualue).

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: find the funotion with hejp of a indegral meau value betw een 4,1] of g(x)=\xl-2

A:

Q: Ex: © Suppise that the fiowing Aransferuntin Conneclğs the lei) and (ti) coordnate Syshems; a4ス?) 2…

A: Given that, ζ=x¯1=ex1+x2x¯2=ex1-x2 To find: a) Jacobian matrix J and J-1 b) Compute J¯

Q: Find the solution of the intial value Problan O y() = importent U2- e ylt) = -V US - 213 pls olve by…

A:

Q: Verify Green's theorem with the given field and path. F(x, y) = (x + y, 2x − y), the path whose…

A:

Q: Suppose f(x, y) = x² + 2æy+ y². Which field plot is Vf? Justify your answer. 鹿

A:

Q: Let C:2-1 in the counterclockwise direction and I= 4. Lnzdz. J= 4. ždz, and K %3D $ tanzdz. For…

A:

Q: andy, sinx asevolutions whow that y, =covX Of yll ty=0 chow that y,=e is quolution Ot uve the meth…

A:

Q: Let C:z-1 in the counterclockwise direction and /= Lnzdz, J $. zdz, and K = %3D . cotzdz. For which…

A:

Q: A liner tragfematin defimeed by a malrıx let IRR be a lineor tras ler malin. defneed by Tv) - Av ;…

A: I have proved Linear transformation using the definition

Q: verif y that the funstio n $(x) VI-x² defined overthe loter val E sati'sfies the coad itions of…

A: Verify rolles theorem

Q: matoix Such that show that Let is Then detx = tt mxn

A:

Q: Let C:z|=1 in the counterclockwise direction and I = 4. Lnzdz, J = $, zdz, and K = $. tanzdz. For…

A:

Q: 5. Verify that the. functrun.u=1/ xy2? satis fies the threendimensianal.place cop.x+Uyy.+Uzz =o %3!…

A: Rrrrrrrl

Q: 9f d prove metric on x then that de de7ined by als is d (x, ) is mateic on x

A: The solution to the given question is explained below.

Q: |Determine whe ther He Veetar Field Con ser vattive, iF it is Find Function For the veetor Field is…

A: Since, a vector field is defined by the function:-F⇀(x,y)=7yxi^ -x7y7j^ +0 k^ -(i)Our Aim is to…

Q: Let C:z|=1 in the counterclockwise direction and I = ¢. Lnzdz, J = $. zdz, and K = $. tanzdz. For…

A:

Q: Please Lgent let VizLi = L3) and w=L4o=2) belongs to spaln (rloV2} %3D termine whether w

A: yes this belongs to span of (V1,V2)

Q: Conotrut a onatn'x whode Columu 8pure (leli2) & whole cli5) 10 is spanned by now &pale in Bpanned by

A: Column space is spanned by 3-dimensional vector. Row space is spanned by 2-dimensional vector.…

Q: Solve using horizantal Slide EX Evaluat..f.x.dA.whak.R.a.the.sgen.in.the figt.…

A: ∫∫R f(x,y) dA= ∫∫R f(x,y) dxdy =∫∫R f(x,y) dydx

Q: ) suppose fle) oa defferentialle funchou on the intervel E-7,1J such that H-7) =4 and fl)=1. Explain…

A: SOLN 3B OKLY AS ASKED

Q: which of the foll ow ing functinn Setisfy Rolle's conditions Frx)=1x-51 on [ 4.7]

A: We have to check that function f(x) =|x-5| is satisfy the Rolle's theorem on [4,7]

Q: Use the method of undeterminad Coefficiento to slve the initial valene proalem : yo +Qy'+5y=cin…

A: The given initial value problem is              y''+2y'+5y=e-tsin(2t)  , y(0)=1, y'(0)=0 We find the…

Q: Let C:z-1 in the counterclockwise direction and / = . Lnzdz, J = , zdz, and K = $. cotzdz. For which…

A:

Q: Queston de Which opton is cornect for the follawing serres? al lo abodely a caningeit 6) F's…

A: The given series is: ∑n=0∞ cos(nπ)6n

Q: the work dane that the field f does to ma (1,2, - 1) to B ( 2,1,v) toral field o F(x,y.Z) =(ces z…

A:

Q: Find te Turer saies onsion of the periodie fun cdon when definition of on eried are -2<tく - 5) 6くt…

A:

Q: Find the divergence. and.cur.f the fallowin.. vecter field: a. È =xej+ ye k. %3D

A:

Q: Let C:z-1 in the counterclockwise direction and/- dz, J = $ Lnzdz, and K-4, tanždz For which…

A: We are asked to find where the Cauchy Goursat theorem applicable. So, first we state the Cauchy…

Q: Find the curl of the vectòr field F(x, y, z) = 2xyzi + 8yzj + 5zk

A: According to our guidelines we are supposed to do only one question.  Kindly repost other question…

Q: Find the divergence of the field. F= 5z e 8xyz i+ 5x e 8xyzj + 5x e 8xyZk div F=O

A:

Q: zez Use Cauchy residue theorem to evaluate . (z'el + ) dz, C: 4x? + y2 = 16. %3D

A: We know that  z2e1πz is analytic throughout the complex plane. Hence by Cauchy's theorem ∮z2e1πzdz=0…

Q: Ex: © Suppise that the fuowing trausfruntiun Cowneciğa the (I') and (xi) coarduate رک سهاور؟ てス4ス)…

A: Given  x¯1=ex1+x2x¯2=ex1-x2 Required Jacobian is…

Q: f Shoo that the interior operat1on has the tollouni ng Propeities. if E, CE2, then interier (E) C…

A:

Q: Findd Fhie boundled by Ahe Cureo area 2. X= 3J-y' and x+Y=3 ーレ

A:

Q: write the following funchon in leums of Heaviside funchions and find FCs). rt, ostく!; 0, 'sts 2;…

A:

Q: Let C:zl-1 in the counterelockwise direction and I = 4, Lnzdz, J = , ždz, and K - $, tanzdz. For…

A: Last optiom is correct  That for only k we can apply cauchy goursat theorem

Q: 7 In the figure MN | OP and ZOST= 73°. %3D Find the measure of ZMTS and ZSTN. M T 73° R. P. A ZMTS…

A: We have to find the angel

Q: Prave by indretion ŽKczkt) z on n that for all integens aoenzl, 2.

A: