Q1: (a) Let the joint p. d. f. of X and Y is f(x, y) = {' find the p.d.f.of W = X + Y. 0≤x≤ y ≤ 1 e. w.

Q: Check it for f(x, y, z) = x²y°z*, that is, compute Vf first, then V x (Vf).

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Q: •/F. Evaluate F. dr. F(x, y) = xi + yj C:r(t) = (9t + 1)i + tj, 0sts1

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Q: Let f(x, y) = xy – y³ + x². where u =. O A. 37 O B. -37 10 37 √10 O D. -37 C. Du(f)(1,2)=?

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Q: A. If z=x + f(u) and u=xy. Show that: x+y- ax =X

A: Question are not correct... I will send this type problem

Q: 3. Let f(x, y) = zsin ry. Find: (a) f(x, y) (b) f(x,y) (c) Syy(x, y) (d) fyz(x, y)

A: Given function is f(x, y) = x sin(xy)

Q: Exercise 2. Prove that dim(null T") = dim(null T) + dim W – dim V and dim(range T") = dim(range T),…

A: We prove dim null T*=dim null T + dim W-dim V and dim range T *=dim range T for every T L(V·W).

Q: Find the exact value of F. dr using any method. b. F(x, y, z)= C is the line segment from (1, 0,…

A: The given vector field is Fx, y, z=yz, xz, xy+2z. We have to find ∫CF·dr.

Q: • Given f(x, y, z) = x² In(x + y- z), find f(2,4, 5). а. 0 b. 1 с. 2 d. 3 O a. b. С. O d.

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Q: ) determine the rate of increase of the infection by sovid19 outhreak size A with respect to p the…

A: Answer

Q: Let X; = tB¡ B,ds. | Is (X,)r20 a F - martingale?

A: Consider the given process:        Xt=tBt-∫0tBsds

Q: 21 - Let V = R3,S = 5 Show that = Span(S) %3D

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Q: 4. Let u = and v = and w = Compute (u x v) x w. %3D 3

A: u×v=ijk-211103=3i-j-6-1+k0-1=3i+7j-k now find u×v×w u×v×w=ijk37-1-111 =7+1i-j3-1+k3+7 =8i-2j+10k

Q: Evaluate F.dr where c is defined by r(t) =; 0≤t≤ 2π

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Q: 3. Let f: R³ R be defined by f(x, y, z) =|| x ||. Find Vf(x, y, z). What is the domain of Vf?

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Q: Find ||F||. F(x, y, z) = i + j + k

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Q: 10. If f(x,y) = xy² + yez² +5, find fr

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Q: S f(t) dx = 0. 1.

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Q: Let w = f(x, y) with f E C² and x =h – kh, y = 4k. Which of the following statements are true?…

A: To find  Which of the given statement is true.

Q: Let F ____ {(a, b]: a, b E Q). Show that a(F) = B(R).

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Q: (2) I Let (x, y) E R X R. Consider the following functions from R? to R? r((x, y)) = (-y, x) and…

A: We have to find the order of r and s. Here rx, y=-y, x and sx, y=x, -y where x, y∈ℝ. First, we have…

Q: B) If f(x.y) x'y? +x*y , find: axdy *Əyər

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Q: Recall the relation between degrees Celsius and degrees Fahrenheit: F = 1.8(C + 32) X and Y are…

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Q: X=(1,0,– 1, – /2)'. Then,||X||3 = ect one: a. b. 2 C. d. V2+2/2

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Q: Let f(x.y) = In (x2y). If f,(2,1)=f,(5,a) what is the value of a? O a. -1 O b. 1 Oc. 0 Od.-2 e. 2

A: From the given problem:   fx,y=lnx2y   fx2,1=fy5,a   Now,   fx=∂f∂x=∂ ∂ xlnx2y=1x2y∂ ∂ xx2y=1x2y·…

Q: Let f(x,y) = In (x2y). If f,(2,1)=f,(5,a) what is the value of a? O a. -1 O b. 1 O.0 O d.-2 O e. 2

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Q: a.Give the joint p.d.f f(x,y) if the 2 balls are drawn with replacement? b.Give the joint p.d.f…

A: As per the guidelines of Bartleby,we are giving here solution of first 3 parts only

Q: Let f(x,y,z) = x² e Vy*+ Compute f(3, - 5,3) and f(5,8, - 6).

A: Given that     f(x,y,z) = x2 e√(y^2+z^2)

Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

Q: Find the pro ection of v on the line with equation

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Q: Let f(x, y, z)= and c(t) = (t, 13/2, t). Compute ff ds y+z

A: The given function is fx,y,z=x+yy+z, and the curve is given by c(t)=t,23t3/2,t. To Evaluate:…