Suppose c is the Ciue r(t) = < cos E , Sint> fay oEt zaM and F = .Evalvate ,Sint> fose O EfLaM J finds uning the the folowing Step ) lomvert the Cine integnal Se fix ds to an Drdinany integuel O Evaluate the integual in Paut @.

Q: Is) Phd an equetian f te tangerut lme et a point C0.0) on the cur ve X= t-144 Aswers: aj 2y-x>0…

A: Topic = Derivative

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A: Diagonalization of the Matrix

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…

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

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A: We will find out the required value.

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A: Draw the graph and find the integral:

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A: Topic:- calculus

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A: which criteria follow to congruent triangle

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Q: OVESTON Prove that A is inveitine if at0 and at b l Gind The pivos 9 A %3D a a

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Q: 4) Osig the inteecal de finiton, find the convo wto a gis diaM fug a of f(+)= cs 2+ 9C-) = e b)…

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A: Given that, w=fx, y And x and y is in polar form that is, x=rcosθy=rsinθ

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A: Given- It can be shown that y1 = e2x and y2 = xe2x are solutions to the differential equation d2ydx2…

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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A: Note: You have not mentioned which question to be solved. Here we are providing answer for 1…

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A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

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

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A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: biveniJN/AN, Dis the midpoint of JA Prove: AJON E A ADM A.

A: Solved below

Q: So lve the se cond order boundary Valye eF problem: Y+y+2yso where y (0) = || and y'lo)s 18

A: The given differential equation is y''+y'+2y=0......(1) with boundary conditions y0=11 and y'0=18…

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Q: Evaluate the triple integral

A: Evaluate: ∬∫ExdV Where E is  x=4y2+4z2       ...(1)x=4                     ...(2) Using (1) and (2)…

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A: a) The poset (P(Z), ⊆)

Q: a. Show that T: 1² → 1² defined by Tx = y = (n), n, = r, is compact where x = (5,) and where0 <r< 1.

A: Show that T: l2→l2 defined by Tx=y=ηj, ηj=rjξj is compact where x=ξj and 0&lt;r&lt;1. Definition:…

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Q: Show that the function u = p(xy) + Vry v(y/x) provides the quation = 0. dy?

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Q: Q2 :- IS fixg)= e then O PYoue that fcag) Continuons d (o,0) that fay =S,x O shaw wether if feay)…

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Q: Use Green's theorem to evaluate s cy? oy)dx + (y²rlo4") dy where Cis s hoon belbw, N y = 2-x² G,1)

A: The given path contains 4 curves: C1:  from (1, 1)  to  (-1, 1)C2:  from (-1, 1)  to  (-1, -2)C3:…

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Q: Let E be the hemisphere described by Oszs V1-x? -y2 and F=Vz? + x2 + y² i+Vz? + x² +v² j+Vz? + x²…

A: We can solve this by gauss divergence theorem

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…

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Q: Qz: IF U=h cx,g )= Lnce+ ě).show that %3D Sy

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Q: U R Given: ZR e ZV Prove: A RST AVUT T.

A: The solution is given in the next step.

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Q: Ginen ahad 2,=J3+Landza=1-J5 Express 21 and 22 in the podar form expsess the namber 1-iJ} aut u!…

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