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Q: Use špheričal čoördiñatės. Evaluate tet dv, where E is the portion of the unit ball x2 + y² + z² s 1…

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Q: Evaluate the iterated ntegral by Lonverting to polor coordinates. 2. zy dx dy 34

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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: w= Pcxiy,Z) = In (x+y+2) ,x= cost, and z = 4VE %3D 2X = y= Sint >use ch ain rule to Rind du in terms…

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Q: The functon T: RsR3 i dyenis ar follous tC") = AV = ]M] %3D 2 -2 os funis Tcr), where v= (2,) as…

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Q: Fnd the emnd tuber pt e dag emema bedagna ttd be dagn by the thn dent Condtion tar agnal ding y ma…

A: Diagonalization of the Matrix

Q: UseThe Culerwe method's Sove the: dy %3D xCi+メ)。 y(0)=3,h=0.2

A: This is a problem of Numerical Analysis.

Q: By making an appropriate change of variables, evaluate the double integral I = - || ( + y)e v°dzdy…

A: Jacobian of the transformation x=g(u,v) and y=h(u,v) is  ∂(x,y)∂(u,v)=∂x∂u∂x∂v∂y∂u∂y∂v Suppose that…

Q: 2) usins Culcuulus for parametrre curres. Show trat the aren of a idis e of radius Ris siren by…

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Q: Find the area Inside the cardioid r=2 cos (6/3) and outside the circle of radius r = vZ centered at…

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Q: HAy check the exs fence Hin at x= 1 of limot of the Lunitie : %3D 2X+/ fex) = %3D

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Q: Evaluate S S f3zdV where E is the solid enclosed by z = 1 and z = x2 +y?

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Q: angleO: Find a Tayler saries for Hhe Sunction fa)= In G) contered at a=I

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Q: Show Whát You KhOw: Properties POSSIBLE AC = 36 cm, and BC = 27 cm. A Verify that DE || AB- 20 cm C…

A: Solve the following

Q: O show mat me Nomal point @ X= a( Coro +o Smo) y= a(8in0-o Cor0) dy Sine %3D ep" of Normal S-ゴ」=…

A: the parametric function is x=a(cosθ+θsinθ) y=asinθ-θcosθ Differentiate each with respect to theta…

Q: 5. Let R be the region in the first quadrant within the circle z² + y? = 4, outside the circle (z –…

A: Region is in the first quadrant :-    Hence, region the region between these circles in above…

Q: A=LDU where D-) then the humber of special solubion s bo Ax =0 is equal a-1/b.e/c.2/d.camt be deubie…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The path integral v- dr, where v = (sin y, x - cos y) and C is the perimeter of the triangle formed…

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Q: II ni msoo sol lo ermov en Area of Base = LA = (P)(n) SA = Ph+2B 13 %3D V = %3D %3D 13 = 216 (の)(の v…

A: Please find the required solution.

Q: 93. which f the follouwing repreeents ene - dimenalional heat Sqeation? 46) du c2 au %3D (d)u + azu

A: Some definitions: Wave equation: ∂2u∂t2=c2∂2u∂x2 Where c∈ℝ is called wave speed. Laplace equation:…

Q: Evaluate the line integral So 7y dr + 3x dy where C is the straight line path from (2, la 7uda + 3z…

A: Introduction: A line integral is an integral that determines the function to be integrated along a…

Q: ) USE THE METHOD OF VARIATON OF PARAMCTERS TO SULVE THE GIVEN ODE 8" +y'= secx Sec'x %3D

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral (5 + Væ…

A: The function is: ∫065+x+123 dxn=10

Q: Find thequahen. perpenditar to i fine -個 epe at OD pr Find tha liit ultpy cen gale (ro a) Po FO…

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Q: Use Greens Theorem to evalua te the line integral Sr -93 dx +x*dy. where C is the positively onented…

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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: Find the temperature u (xjt). in a bar of Length t which is perfectly insulated everywhere including…

A: temperature distribution u(x,t), follow the partial differential equationdudt = d2udx2   ,…

Q: Evaluate | CurlF nds F(x,v,z) = - yzi + xzj – xyk, and S is that part of the cylinder 4= x² + y²…

A: Given function is  Fx,y,z=yzi+xzj-xyk To evaluate ∬SCurlF·nds where S is the part of the cylinder…

Q: If the region R is bounded between two circles 961 x² + y? = 4, x² + y? then we have: 2л 3 sin(Vx2 +…

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Q: 2 Evaluate the fullowng cartesianntegrat changing theminte equivalent Pelarintegrals: Fー dxdy 2-

A: We have to find the double integral using polar coordinates.

Q: (b) f(u) = tan(arccos u). FRAS SER UNIVE ERS %3D ERSI TY OF fficial que s test question question ion

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Q: to find 2y dx-xdy, Use where C is the green's theorem the the eircle wi'th radivs 4 Centered at…

A:

Q: Solve the DE, dy =y²-a? E, = , using the homogeneous method. ry (a) Hint: Rewrite the RHS as 2 -…

A: dydx=y2-x2xy⇒dydx=y2xy-x2xy⇒dydx=yx-xy⇒dydx=yx-yx-1 Now put, y=vx⇒dydx=v+x·dvdx

Q: Show that the area of the surface of the solid generated by revolving the cardie r = a(1- cos 0)…

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Q: ae e drea under the curvé y=*from2-2to2 using a Rightt Endpoint approximation with 6 subdivisions..

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Q: 10- Evaluate JJI where E is the region that lies inside the cylinder Vx2 + y?dV E x? + y? = = 16 and…

A: Here we use polar coordinate and Jacobian .

Q: 3. Evaluate the integral cosh ™z dz, z(z? + 1) Izl=2 where the circle |z| = 2 is described in the…

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Q: If the region R is bounded between two circles x² + y = 4, x² + y = 9, then we have: sin(Vx2 + y?)…

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Q: The cable AB carries a tension of 400 N. Determine the moment about O (positive if counterclockwise,…

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Q: 4) By Diskuethod Detremin the volup Hiw Dx=1 and lnes y=1 aboat x=0 2) fex) = x? and line y:1 in the…

A: Given

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…

Q: Evaluate the line integral fx ds between (4,0) and (0,4), where C is the circle of radius 4 centred…

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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>0       =0.000004e-0.02xx2,…

Q: (2,2) b) Evaluate o x*y dx + x dy, shown in adjacent figure using green's theorem. where c is…

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Q: let A and B be matiices of Con det A) = -1 find the Valué of Cdet(z AT) - dct(-2B )) LA Pproxi mate…

A: Given:- det(A) =-1/2   ,  det(B) =2/3 To find:- [det(AT/5) -det(-2B-1)]2

Q: The path integral fv· dr, where v = (sin y, x – cos y) and C is the perimeter of the triangle formed…

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Q: 8. Use Green's Theorem to evaluate px*dx+xydy where C is the triangle with vertices (0,0), (1,0),…

A: As we know from the Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA And The expression for the equation of…

Q: Use Green’s Theorem to evaluate ∮C squre toot of (1 + x^2)dx + 14x dy, where C is the triangle from…

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Q: Ô dlen proplical auolyir to alve Use Max

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Q: Find dyldy and xz4 Sint, y² Scost, OCtca24 For which vakes Of t is Hhe cure concave puars? anguer n…

A: x=4sint  , y=5cost

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.