T is self adjoint if (Tx, y>= (x, Ty> o > |(Kr.x>|| o

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: Let f (x, y) = 1 5+√x²+y²-1 Then range of f is:

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Q: Solve for the General Solution of the given first-ordered Lineor DE : X lx² +1)y'+2y= (x?+1) %3D

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Q: Show that if (xig)m.u. is re<rz , it is 8\x,r) C Blxirs] for Jx EX.

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Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x:x>5}. Find d. A-D e. A x B f. BxB g.…

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Q: B)Is w = Ze² analytical function or not?

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Q: How, Form P.D.E. from: a (3) Ucx,y) = (x²+a)lytb)

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Q: Determine the length of x = 4(3 + y)* , 1<y<4 %3D

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Q: TF x and y are orthon ormal rectors then Pind Value of Ilx+y12 - ||x-Y2

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Q: Evaluate y ds, C: x = t², y = t, - 1<t < 9 |3D (325)-(5)를 1 12

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Q: Let X=(1,0, – 1, - /2)'. Then, ||X||, =| Select one: а. -1- V3 b. -V3 O C. 2 +/2 d. -V2

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Q: For which values of ß does {(1,0, ß),(1,2,–3)(B,1,0)} span R'?

A: If spans the same subset of R³, the vectors must be linearly dependent to each other.    Therefore,…

Q: Find general solution of U" + U = 0.

A: Given differentiation equation is U''+U=0. We have to find the general solution of the given…

Q: 4. If /(r.y)=- , find f, and f,. V+y

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Q: Determine the length of x = 3+ (y – 2)², 4<x< 19

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Q: Which graph corresponds to the function given? h(x) = {x², x 1

A: Here we have to draw the graph of the function.

Q: Se xye" dy, C. x- , y-, z- , 0 <te1

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Q: If fxy (x, y) = , ,0 2) =

A: Given,fXY(x,y)=x+y27 ; 0&lt;x&lt;2 , 3&lt;y&lt;5

Q: uppose ū = (1, −3,−1) and v = (1, -5, -5). Then:

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Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

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Q: Show that if (x.g) m. is re<rz, it is 8lx,r) C Blx,g) for x Ex. U.

A: Metric or Distance: A metric or distance is a function ρ :X×X→ℝ such that ρx, y represents the…

Q: Let X=(1,0, – 1,-/2)'. Then, ||X||2 = Select one:

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Q: If f.(x, y) = 13x + 8y + 11, || f.(3, 2) = a. b. f„(5, 2)

A: Given, fx(x,y) = 13x + 8y + 11 a). fx(3,2) = 13*3 + 8*2 + 11 = 39+16+11 =&gt; fx(3,2) = 66

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: Let x = (m , 1 , 0 , -2)", m > 0 and ||x|l2 = v30, then m = Select one: а. 4 b. 5 с. 6 d. 7

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Q: Find y" if y = x + (x + 2)3 when x = 1 Оa. 16 O b.9 Ос. 18 O d.28

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Q: fluu) is a function, fl13|=0 fal-1.31=2 ,fg(-1.3) =-3 glxiy.z)=f(xyz,xzyzz?) So Vg(1,-1,1)? %3D

A: Gradient of the function w=f(x,y,z)  is given by ∇f=∂f∂x,∂f∂y,∂f∂z Chain rule of derivative: Let us…

Q: b) y"+y=0.

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Q: Let X-(1,0,- 1,-V2). Then, |X|l3 = %3D Select one: a. 2+2/2 O b. C. 2 O d. arch

A: Answer :