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Q: ®. *,(t)=l, tilt)=t, Xglt) =t² Let [oD. Use Gran-Schridlt on er thogonolize e, 2) process to

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Q: Compute the line integral (Баллов: 2) Jo ds, Cis the right half of circle x2 + y 16 (counter…

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Q: Show tuat a fuinchon fiR?>Rlefined by 3ں۔x5 ,ie (xxy]#Cojo) f cary)e je xcy=o Is continuous at (o,e)

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Q: Consider the region in the Second and third awadrants between the sirttt Circles xty?-4 and…

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Q: If R is the region boundeb by the square a|+|y = 1 then ffR(y-2)dA is equal

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Q: Assume that D is bounded by the lines y = x +1, y = x, x = 0, and æ = 1. Calculate: S Sp e22 dA =…

A: Given : y=x , y=x+1 x=0, x=1 To find integration of e²² da

Q: he area bounded by the curve y = 3Vz and the lines z = 5 and z = 9 above the r – aris is_ quare…

A: Find the area of bounded curve with line x=5 and x= 9 above x-axis

Q: 3 Show thot tfe fundion fae Ax +26T* +C with A = AT E IR E IR", CE IR is strongly Convex if and only…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: A hransfoomation is definad by Hhe axa matox A=-a b-a atb Ifois an odd imtreger, prove %3D ushere a…

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Q: 2uppore that tuo - dimensional, contiruous Mandom uariable (x,4) fa's yont" P•d.«b. gien by : ,…

A: Joint Probability Distribution: Let X and Y be two continuous random variables defined over the…

Q: C Find the firet order parhal derivohve of fx,y,2). e W y-10y²23+ 43x hCs, t) =° t*In ts) + 32 4,5…

A: We want to find first order partial derivative of the given functions.

Q: Find to the the equation du green funclion corresponding pula)=fex) conditions U(o) =0 with and…

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Q: d, d': xxx-R be two metrices on x that Satisfy following for every nEX and >0 7>0 st. Bai (x, S) C…

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Q: 28. Given: WX ZY and Zs Z and Y are supplementary WXYZ is a parallelogram Prove: ZRYS RVST

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Q: 22. Compute the contour integral (Баллов: 2) Sof (2) dz, z E C, if f (z) = and path is semicircle z…

A: Topic:- application of integration

Q: 10. Given: YX = ZX WX bisects ZYXZ Prove: AWYX AWZX

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Q: Let X,Y,T be dotined poinds. Show that if Te X Ÿ then XY = %3D

A: It is given that on considering that let X,Y,T be the distinct points The objective is to show that…

Q: Given: XZ is al bisector of WY Prove: AWYZ is isosceles.

A: Given,  A ∆WYZ with perpendicular bisector of WY  is   XZ.  We have to prove  ∆WYZ is isosceles.

Q: and y have density flay)=82y tor Find ECX14) and ECYIX) リフズ7679 %3D

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Q: 4. (45pt) Compute the following contour integrals and give reasoning. 2z dz (a) Jc 7(z+4) where C is…

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Q: The area bounded by the curve y = 7x and the lines z= 2 and =9 above the z-aris is O 539.00 square…

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Q: If L is a line through 0 and if f is the orthogonal projection of y onto L, then || F|| gives the…

A: Option B is correct.

Q: If the region R is bounded between two circles x² + y? = 1, x + = 4, then we have: ev+ dr do dA = +…

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Q: O By using Green's theorem, evaluate $ (In (2²) + æy² – y²) dæ + (ev + x²y – 3ry) dy, where C is the…

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Q: be the limear troumformation T:R¬R? ([:]) = [], T(C:1) - [:]. et, ㅜ Buch that %3D et, Them ([:]) +…

A: The encircled term is  xy=y11+14x-y440 Theorem: Let v be a vector space of dimension n. Then any…

Q: 10) Use Green's Theorem to eualuate S+10ny +y?)dx + l6xy+ 5a²) dy Toxy+ sa?) dy where C is the…

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Q: 7. let E be the reyion bounded by curve 2+2 in the yex? fint quadant let u xy, Vzy-x d Czry)…

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Q: 2 Use Green's Theorem to evaluate Jx*ydx-xy dy, where C is the circle 2+ y? – 2601 with…

A: Let be the vector field and C be the boundary of the region D. The Green's theorem states that .

Q: Find the solution of the differenhal equahon not Sothsfes the given inital condiion dP at

A: Given.The differential equation is

Q: consider the curue desoribed by 2y"-x²_4y vevity that the foint (4-25 les on this o8 wrE andd find…

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Q: Find the orthogonal traiectories ofthe one-narameter fomilyy2 - v2

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Q: Consider d Hentiel eps %3D whese, ? is di fential oberator on finction space de fined fox holadary…

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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: Autocorrelation is simply the cross correlation  of a function with itself, For the first function…

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:…

Q: Jraen fusk hon conespaaday to o d'u z ul) = flx). dx² Find the the egualido for conespoodiang to…

A: Given differential equation is d2udx2+u(x)=f(x)                   (1) boundary conditions are…

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A: Given that the integral,

Q: If C is the line segment from (1, 4, 2) to (3, 2, 1), evaluate the line integral y+ 2) ds.

A: Express the line segment in its parametric form and then use the formula below to evaluate the line…

Q: Let X - Y (3, 0.02). Given Ttx = 300 calculated by the Esscher Premium Principl %3D

A: From the given information, X~γ3, 0.02 fx=0.023γ3e-0.02xx3-1, x&gt;0       =0.000004e-0.02xx2,…

Q: 13 ABCD is a trapecium with ABDC. A line parallel to AC intersects AB at X at Y Prove that ar…

A: Since you have asked multiple question, As per our policy we will solve the first question for you.…

Q: If the region R is bounded between two circles x2 +y? = 1 and x²+y? = 16 , then we have: J| x²+y?)…

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Q: Given: ARST = AXYZ; SK bisects ZRST; K YL bisects 2XYZ. Prove: SK = YL S

A: Prove SK≅YL.

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: => For The Wbech Ualuo of E doas the Martrix イK %3D have one roal eaomalue of Mutiplicty?? k =

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Q: Prove that A Unitoy matylre U is Yemem bereel as Svuare Matsin whose colounn Vecto 8 have Cume theio…

A: The solution is in step 2

Q: ral by making an appropriate change of variabl re R is the region enclosed by the lines y = 6x

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Q: z is a complex variable z=x+iy pic attached with question

A: To establish the analycity of the  function under the given conditions.

Q: he region bounded by the cylinder x2 + y2 = 9 and the planes z=0 and x +z =9 O 243 O 81T 27TT 729TT

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Q: Suppose 4 Let that S be lines bc and u = x -y the y 571 x are related and 14 region > y = to u ar…

A: Introduction: A finite collection of equations for which we searched for the common solutions is…