tan" (x)) Determime the giwen serves is convergent or duergent. Show and State the theorem/test ypu used n-I rintz)

Q: Show that the function u(z, t) : satisfies ua = %3D %3D a2t2-2

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Q: Use the chain rule to find where g(u,v) = f (x(u,v),y(u,v)), f(x,y)=xy³ -4x² , ög ди x(и, у) -и*…

A:

Q: ield F = (A, B, C) such that A = 2zx, B = 3z + 2y, 0,0,0) = 1 and C is independent of

A: We have to find the following conditions according to the given information

Q: Iculate O F- dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

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Q: prs is Linearly independent. please prove it. z set A is orthogonal if Por every Xy>X_eA, we have 2.

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Q: Describe how to find the Jacobian of x and y with respect to u and v for x = g(u, v) and y = h(u,…

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Q: 2- find if z = x + 2メッ ze %3D U COSU = u sinv

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Q: If la,} and {b„} are divergent then {a, + b,} is divergent. True False

A: Given: an and bn are divergent . The objective is to state whether an+bn is divergent is true or…

Q: Q2. (e) Verify that the Cauchy-Schwarz inequality holds. įu=(-3,1,0), v=(2,-1,3) u u=(0,2,2,1),…

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Q: Use the chain rule to evaluate fu and f, at (u,v)=(2,-2) where f(x,y,z)=y³+xz² and x=x(u,v)=u+v²,…

A: Concept: The chain rule for the function f (x,y,z) is  dfdu=∂f∂x∂x∂u+∂f∂y∂y∂u+∂f∂z∂z∂u…

Q: ) If ƒ(x,y) = 3x²y + cosy+ ysinx – e2x then verify fxy = fyx

A: fx and fy are the partial deferential of function w.r.t x and y respectively. Then fxy is the…

Q: U = kuzx for 0 0, u(0, t) = u(L, t) = 0, u(x, 0) = x(L – x)

A: Given that, ut=kuxx , 0<x<L, t>0u0, t=uL,t=0ux, 0=xL-x This is  the heat conduction problem…

Q: ¸(1+ h)² −1 lim h→0 h using the squeeze Theor

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Q: Use chain rule to find az at (u, v) = (1, 1) if

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Q: Two functions u and r of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and -…

A: Given that the functions u and v are said to satisfy Cauchy Riemann equations if ux=vy   and uy=-vx…

Q: Find the Jacobian of following functions f(x,y,z) = 3xy – yz + 2y³z² – 5xyz³ g(x,y, z) = xyz – x³yz…

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Q: Let UsX +Sinx Deter of X 0n [0,)where ļ Find . derivalire fa 2x+1 x²+7 te tn 6x+

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Q: cet 1-R be funchion suchtheab fox)= x2 hat fis R-integrable provet andfetermine the Vile of

A: Introduction: The Riemann Integral was invented by mathematician Bernhard Riemann and was the first…

Q: Verify the Cauchy-Schwarz Inequality for u = (1, −1, 3) and v = (2, 0, −1).

A: u = (1, −1, 3) and v = (2, 0, −1) To verify the Cauchy-Schwartz Inequality for the given set of…

Q: 4Ux+Uy=U² , U(x,0)=1/1+x²

A: In the given partial differential equation with the given initial condition. 4ux+uy=u2u(x,0)=11+x2

Q: Using the stability criterion by means of bilinear transform (Tustin), find if the system is it…

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Q: Prove that Ix I - I y I ≤ I x - y I.

A: We have to prove that  x-y≤x-y We know, x+y≤x+y Then,  x=x-y+y⇒x=x-y+y≤x-y+y⇒x-y≤x-y

Q: I + x

A:

Q: Find the Wronskian Determinate of g(x) = sinx f(x) = x and %3D %3D اخترأحد الخيارات W(f, g) = x cosx…

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Q: let z- 57 dy .. dy By chain Ruie

A: The objective is to find the second derivative using chain rule.

Q: Cramer kuralını kullanarak verilen denklem sistemini ÇÖzümleyiniz. 2x + 3y + 4z = 53, %3D 3x + 5y –…

A: We have to use Cramer's rule to solve the following system-

Q: Ques. 3: Check whether the operator T: R2 → R² defined by T(x,y) = (y,x) is linear. Moreover if T is…

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Q: lim (2,y)→(1,0) X + y – 1 Determine which of the following paths is not valid to check the existence…

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Q: 4)Determine the jacobian u = x (1– r²) i, v= y (1- r²) w = z (1 – r²) /hen r2 = x² + y2 + z2…

A: Given u=x1-r2-1/2, v=y1-r2-1/2 and w=z1-r2-1/2 where r2=x2+y2+z2…

Q: azu Q5) Find u such that ax2 with u(x,0) = 0.5x2, u(x, 10) = 0, u(0, y) = 0, = 0 %3D u(20, y) = 1…

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Q: 1- -Н(y)-Н(yх) Prove that 2- H(x,y) = H(y) + H(x\y) 3- H(x,y) = H(x) + H(y}x) 4- Н(х., у) %3DН(х) +…

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Q: Prove non-existence of limit cycles for the system i = y? – x, ý = -y + 2xy + 2y by a) using index…

A: PART A The given system is : x˙=y2-xy˙=-y3+2xy+2y Now, the equations will be , x˙=0y2-x=0x=y2 Also…

Q: Use of Cramer's Rule 2x, – 3x, = 5 X +x, = 5 [1 1][x, X

A:

Q: s lineax diggerential Solve nonhomogene ous equation using propesty of diggerential operator I…

A: Auxiliary equation of given ODE is  m3-2m-1=0m2-m-1m+1=0 So we have Complementary solution is…

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

A: Here we have to use cramer rule for solving the system of linear equations

Q: azu azu (a) Verify that u satisfies ax2 = = 0 , if u = e* sin y. ay?

A: NOTE:Kindly repost the other question as a separate question.

Q: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

Q: Exercise 5 3x + ax + b x² +1 Conşider the function f that is defined over IR as: f(x) = Where a and…

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Q: Prove that arctan x + arctan y = arctan(x + y) / (1 − xy),  xy ≠ 1.                   Use the…

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Q: 3- Verify the properties (HINT Use integration by parts) F[ux] = iF[u] F[uxx] = -²F[u]

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Q: If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y – 2, z – x, x – y), then х, х — у), then ||…

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Q: Let T: R² → R² be the linear operator given by 7 ] - ([ ; ) = [ - {|- } {} } -x + 2y Зх + у and let…

A: We can solve this using given information

Q: Ques. 3: Check whether the operator T: R2 → R2 defined by T(x, y) = (y,x) is linear. Moreover if T…

A: A mapping T:R2→R2 is a linear transformation if and only if a) T(u)+T(v) = T(u+v) b) T(cu) = cT(u)…

Q: vVr ITe uruit 10 dEscribe EUCN TraNSTOPmUTON. 本y A 9) A' Z' Z'. K N' K' A n'. K. K' Rule: 12)

A: The given figure AZNK translated into A'Z'N'K'

Q: 6. Let f(u, v) = u sin(v) – v cos(u) and u(r,y) = r² – ry² v(r, y) = y – r Find af af and both by…

A: We need to find the derivatives using direct substitution and by chain rule . Now , we have ,…

Q: Q)is a) x^2=y^3 reflexive antisymmetric Transitive  Explain it correctly,solve only when know…

A: We have to find the correct option

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.