3. Choose whether the following statements are true or false: (a) Ax.ly.y x is a-equivalent to Af.An.n f A. True / B. False (b) Ay.y x is a-equivalent to Ax.x y A. True / B. False

Q: If f(x,y)= Iny, then Vf(x,y)= :- Select one: O True False

A: We know that, gradient is a vector function. ∇fx,y=fxi^+fyj^

Q: Consider the relationship R CN x N, R(x, y) holds iff (/a /9) E N. True or False R is reflexive true…

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Q: if f(z) = (ax – x³ + 3xy³)+ (by – 3x²y+ y') is anal ytic , then the value of a and is

A: We have , f(z) = ax - x3 + 3xy2 + iby - 3x2y + y3 We have given that ,  f  is analytic function.…

Q: If f(x, y) dA > 0, then f(x, y) > 0 for all (x, y) in D. True False

A: Given statement, If ∫∫Df(x,y)dA≥0 then fx,y≥0 for all x,y∈D. The objective is tell whether the…

Q: af If f(x) = x²yz + xy³z than is дудz x?yz + xy°z yz + y°z Option 1 Option 2 x? + 3xy? y? + 3xy?…

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Q: Give an e xam Ple of (T, m') ameasurable SPa ce F; x → T {E & CX : fCE) ET3 m is not

A: Given, Τ, m a mesurable space fi:X→Τ , m=E⊆X: f(E)∈Τm is not a σ-algebra on X.

Q: SL (e,9) f(x, y) = dx dy f(x, y) dy da 0. 0. 0. O True O False

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Q: --Let f(x, y, z) = x²y z +2ye²+7, find Se Əx = ? af =? ду =? axdz

A: f(x,y,z) = x2yz +2yez +7 df/dx = 2xyz  df/dy = x2z + 2ez df/dz = x2y +2yez d2f/dxdz = 2xy

Q: 15. f(x, y) = xy /x² + y V9 – x² – y? 16. f(x, y) ▪ x + 2y + y? x² – y? 17. f(x, y) *

A: 1.  fx,y=xyx2+y2.  fx,y=9-x2-y2x+2y3.  fx,y=x2+y2x2-y2

Q: If f(x, y) 3x+7y af then is given by: (3x–7y) 21y (За — 7у)? 21y (3x–7y)² - 42y (За — 7у)2 42y…

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Q: (1, O<y<2x<2 Given f(x, y) = 0, otherwise 1 show that E(Y]x) = x and E(X\y) = %3D 4 2

A: The joint distribution is given by, f(x,y) = 1,0&lt;y&lt;2x&lt;20otherwise Note that,…

Q: evaluated at fo as follows. 1 0.5 0.2

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Q: If f(x, y) = 7xey + 7y Inx, then is given by: дудх O 49e5y + 7/x 35eby + 7/x O 25e5y + 7/x O 35e5y +…

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Q: Let f(x,y) = ax + by2 af where a and b are constants. If of at x = 1 and %3D ху y 2, then the…

A: Introduction :

Q: Let A = {x E R : 2 < x < 3} and B = {r €R: -1<r< 2}. Prove that |A| = |B|.

A: To prove this result we first show a objective map from [-1,2] to [2,3]. Then (2,3) is uncountable…

Q: 5. If z = In , then determine if the following statement is true or false. Justify your answer. a²z…

A: Solve the following

Q: 1 If (x, y)= find f, and f,. Vx? x²+y²

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Q: It is always the case that f(x, y) dydx = f(x, y) dædy. OTrue False

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Q: ate f(c(t)) and ds = ||c'(t)|| i te Sc ƒ(x,y, z) ds.

A: Introduction: A line integral is a type of integral in calculus in which the function to be…

Q: If f (z, y) — е"у, then fr (1, In (3)) —??? (а) е (b) e³ (с) 1/3 (а) 3 (е) 3ln (3)

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Q: Evaluate f(x, y, z) dS. f(x, y, z) = XY S: z = x2 + y2, 4 < x2 + y2 < 16

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Q: Find ax Je ar az nd 을. if Je 1. 2. f(x. y) = Vy – x´ %3D - 6. f(x. y) = y/x² 8. f(x, y) = V9 – x² –…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: 1. Evaluate xy Va? + y? dy dr

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

Q: Consider f(x, y) = x³ + 2ry + y. Compute the following: (b)

A: Answer and explanation is given below.. Simply do partial derivative with respect to x and y.

Q: If f(x, y) = (x³ + 4y2)3, find and ax ay af Əx af ду II II

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Q: Consider the relationship R C N x N, R(x, y) holds iff (/æ /T) E N. True or False R is irreflexive…

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

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

Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

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Q: Let x be a c.r.v., the E(x4) can be founded by xf(x) dx. O True False

A: Given problem Given that   Let x be a c.r.v., the E( x4 ) can be bounded by ∫-∞∞xf(x) dx   Ans)…

Q: 1 Let D = (x, y) : 9 < x² + y² < 25, –y < x < V3 /| 4æydA Evaluate

A: Consider the region D as shown in the figure below: Here, the objective is to find the double…

Q: Q₂. if z=f(x+ct) + g(x-(t) then show that C²Z = Ztt XX

A: Given function: z=fx+ct+gx-ct We have to prove that, c2zxx=ztt. We know that, daxndx=anxn-1

Q: 1. Given f(x, y) = 4x³y², evaluate f;(1, y) and fy(x, 2).

A: We know that partial derivative of f with respect to x is denoted by fx  and partial derivative of f…

Q: 21. If F(x)= [ VP +1 dr, then F'(2) = %3D (A) -3 (В) -2 (C) 2 (D) 3 (E) 18

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Q: Let f(x, y) = y? – x? and g(x, y) = e²+y. Verify that div(ƒVg) = fV²g+ VƒVg.

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Q: I. Find the absolute max and min for f(x,y) = xy² on D ={(x,y): x >0,y > 0, x² + y? < 3}. Justify…

A: Given- f(x,y)=xy2  to find - Absolute maxima and minima for the given function if onD={(x,y):…

Q: Q5/ If w = f(x,y),x = rcos0,y = rsin0 show that: af af 5² + 1 dw Əw. -)² + ar r2 a0 дө

A: The chain rule can be used to calculate the derivative of the complex functions. The function which…

Q: If f(x, y) = e + e", then .Vf(x, y) = (0, e') :Select one TrueO False

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Q: (c) If f(x) = x + v2 – x and g(u) = u + v2 – u, is it true that f = g? %3D (d) If x² – x f (x) and…

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Q: a) Is it reasonable to assume X; and Y; are independent? b) Is it reasonable to assume X; is…

A: According to the answering guidelines,  we can answer only three subparts of a question and the rest…

Q: Suppose that X, Y C U. If Pr(X) = 0.4, Pr(Y) = 0.22, and Pr(XnY) = 0.07, what is Pr(X' U Y)? %3D

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Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

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Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf(2, –1, 1) = - A) * V3 B) 11 C) V3 D) E)

A: The given function is:    f(x,y,z)=ln2+x2-2y2-3z

Q: Show that if Y = ax+ b (a ≠ O),then Corr(X, Y) =+1or -1. Under what conditions will p =+1?

A: Assume that X has has nonzero variance, since otherwise the correlation coefficient would be 0,…

Q: . If z = f (x, y), where x = e" - e and y = e - e", show that TM UT az x: az az az dy ax UTM UTM UTM…

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Q: Q4 * If f(z) = z? ;z = x + iy Show me u(x, y) ;v(x, y) Determine ux; Vy|

A: