Task 6 (Sobolev spaces) Let pe (1, 00), f e W((a, b)). Show that af = 0 f= const a.e. in (a, b).

Q: Let f(z, y) = zy-y+a?. D.((1,2) =? where u=. OA- O B. -37 Oc- 37 OD.

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Q: A vector y in Rn can also be viewed as an n × 1matrix Y = (y). Show that ||Y||2 = ||y||2

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Q: Use Stoke's Theorem to evaluate Į F· dr where F (x, y, =) = , and C is the triangle with C vertices…

A: given Fx,y,z=z2,y2,xy ⇒Fx,y,z=z2i^+y2j^+xyk^ and a traingle C with vertices 1,0,0 ,0,1,0 ,0,0,2 to…

Q: Find the domain and range of:

A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: ху f(x,y,z) =- х+у+z

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Q: Find the average value of f(x, y) over the plane region R.

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Q: Ut + 4tuz – 2u e', x E R, t > 0 u(x, 0) xe- , x E R. Find u(x, 1).

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Q: zy? (z, v) + (0, 0) f(x, v) (z, u) = (0, 0) %3D

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Q: If f(x, y) = xsiny + e" , then V f(x, y) = (0, e'). Select one: True OFalse

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Let f(r, y) = (3 – y)". Then %3D drdy drðydr

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Q: Va vector space? Show the detailed solution for each property.

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Q: a) What is the dimension of {(x, y) E R² : x + y = 0}?

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Q: Let f (x, y) = 9e2xy what is fryx (x,y) =? %3D

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Q: f(z) = Im z is continuous 0 صواب ihi O

A: True

Q: Find a linear transformation T:

A: Consider the provided information, T11=23   and T1-1=05 Find a linear transformation T. We can put…

Q: a) Rewrite the expression P= f(Q, D, 52, P,H) in dimensionless form by using Pi- theorem, where P is…

A: image is attached

Q: af (x,y) f(x, y)=xe"+* 5 у, Х (а) Сompute y af(x,y) X f(x, y)=xe³"+* ,5 у (b) Compute ду y

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Q: Let FE R?. Show that F = ő if and only if F · Ä = 0 for all vectors à E R². (This is a proof, be…

A: We have⇒    F→=0→⇒ F→.A→=0→.A→=0  for all vectors A→⇐ F→.A→=0    (f1i+f2j).(a1i+a2j)=0f1a1+f2a2=0…

Q: f(2) — и(х, у) + jo(x, y) и(х, у) — е% сos x — х f (0) = 1

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Q: af (2,0) ay f(x, y) 3D хетУ + 5у%; af (2, 0) = Əy

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Q: This question is from partial differential equation please sir g give me answer immediately

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Q: Let f (z) =iz-7x. Which of the following is correct ? oiu, = -7 v, i u =- y i u =7 v oi4 = - 7 v iu=…

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Q: What is the dimension of {(x, y, z) E R³ : x +y+z = 0}?

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Q: af Find if f(x,y) = ysin xy

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Q: Evaluate ſ √x² + y²dxdy over the triangle with corners (0,0), (4,4), and (4,0) using x = u, y = uv.

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Q: Given f(z, y) = 6z° – z'y 3y, find f-(z, y) = Preview f,(z, y) =| Preview fa.(z, y) = Preview fay(2,…

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Q: im(z,v) →(0,0) F(x, y).

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Q: Find f, and f, and evaluate each at the given point. y' f(x, y) ), (8, -8) = arctan fx(x, y) = f,(x,…

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Q: Evaluate F. dr. F(x, y) %3D хі + yi C: r(t) (5t + 1)i + tj, 0 sts1

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Q: a) If W =(x,y), where x v²-g' and y 2vg calculate W+ %3D

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Let f (x,y) = e**ytan (x + y), find дудх

A: Explanation of the solution is given below...

Q: f(x, y) %3D 3ху + у? (а) f(x + Дх, у) f(x, у + Ду) — f(x, у) - (b) Ду Зх + 2y + Ду Ду # 0

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Q: u e R is called an upper bound of S if u <S vS e S صواب ihi

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Q: Evaluate F. dr. F(x, y) = xi + yi C: r(t) = (3t + 4)i + tj, Ostsi

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Q: Find fayr. f(x, y, z) = r*y"s* + xy' + y°z

A: The given function f(x,y,z)=x3y5z8+xy9+y3z

Q: If F = xzi + xyzj – y?k, find i. V · F ii. V × F iii. div(curl F)

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Q: Given f(z, y, z) = /1z2 + 3y? + 222, find %3D f-(z, y, 2) =| f,(z, y, 2) = f.(z, y, z) =

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Q: "ind where f(x, y, z) = e²´y and x = Vuv, y = ; %3D dv

A: To find the partial derivative using chain rule

Q: f(x, y) = e&z– 4y af af ду

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Q: af Find if f(x,y) = y sin xy ax %3D

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Q: O Let f(x, y) = (5æ – y)°. Then -

A: We can find the required partial derivatives as below

Q: a) What does ds(u, v) measure? (b) What does dm(u, v) measure?

A: To find: a) measure of ds(u, v) . (b) measure of dm(u, v).

Q: a) a = 0,10, dfy = 8, dfp = 10. Fg = %3D %3D b) a = 0.10, dfy = 8, dfp = 6. Fo = %3D %3D c)a = 0.10,…

A: Here critical values from F distribution table

Q: B) Use Green's Theorem to evaluate F-dr, where C is the triangle with vertices (0, 0) (3,0) and (3,…

A: Explained below

Q: Find f,(x, y) and f,(", y) for f(x, y) = (82³ – 3y?)". f.(x, y) = Preview f,(x, y) = Preview

A: Given function is

Q: Use Hölder inequality to prove |lulla < ||u||3||u||;-1 for u e L" (N) 1-2 Where p <q <r and p r

A: It is given that u∈LrΩ where, p≤q≤r and 1q=λp+1-λr.

Q: Let f (z) =iz - 7x. Which of the following is correct ? oi4 = - 7 v, и 3D — olu =7 v oi4 = - 7 v,…

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Q: f(x, y, z) = 4x²y - 8xyz + 10yz? (x, y, z) = %3D x. Y. z) = f,(x, y, z) =

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Q: et V xu u = (1,3,-3), v = (4,0,2) e l -3 %3D ......

A: Given:            u=1,3,-3            v=4,0,2 The cross product of two vectors is…