The joint p.d.f. of the r.v.'s X and Y is given by fx,y (x, y) = (x + y²), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0, otherwise.

Q: If X = x „then W(x1(t), x,(t)) = 10 Select one: O a. ce- а. O b. ct C. c t? d. ce'

A: We will use basic knowledge of Wronskian for a II order linear homogeneous ODE. WE convert the above…

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: Consider the exact U (x,y) that 2x + f = x taf Statistics. au aa au DDE (2x+ f) dx + (x + ² f) df =…

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Q: O Find Vf, where f(x, y, z) = = e¯(ax+by+cz) with a, b, c some constants.

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Q: Find V x (V × F) if F(x, y, z) = xyj+ 6xyz k. V × (V × F) =

A: Given: Fx,y,z=xy j+6xyz k To find the  cross product of ∇×∇×F

Q: Which of the following is the parent function for a) f(x) = x b) flx) = x c) fx) = Ix| d) flx) = Vx

A: Given function is y=23x2. We have to find the parent function of y=23x2. The parent function is…

Q: Find fx and fy for f(x,y) = y In (x + 8y). II

A: Step 1:​f(x,y)=yln(x+8y)​Step…

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: Let Find A = x³y 1-2xz] + 2yz k Vx(VxA).

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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 O.O Od.-2 O e. 2

A: For calculating the partial derivative we need to assume one variable as constant and differentiate…

Q: Which of the following expressions are not valid? Why? (a) [ f* 1(x, y) dy dz [T (c) [[1(x, y) dy de…

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Q: Find fyzy. 9,8 f(x, y) = x°y³ – 8x*y + x f yry yxY ||

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Q: Let f(x,y) = In ( x2 + y). If fy(2,a)=fy- 1, 2), what is the value of a? а. 3 O b.7 О с. 8 d. 6 O e.…

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Q: Let f(x,y) = In (x³y). If fx(6,2)=fy(5,a) what is the value of a? а. 1 O b.-1 O C. 0 O d. 2 O e. -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: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

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Q: Let f(x, y, z) = yexyz², then fxz is: Select one: O (4xyz + 2x²y³z²)exyz² O None of these O (2xy² +…

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Q: Suppose f(x, y) = xy² + 3. Determine each of the following: f(0, -2)= f(-2,0)= f(0,0)= f(-3,-2)=…

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Q: Find fx and fy for f(x,y) = y In (x + 8y). II

A: To provide what is best and to understand more about the students concerns for their studies.

Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: find an antiderivative Fon of the function fox)=5sinX such that FCO)=1.

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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 O.0 O d.-2 O e. 2

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Q: 2. Show that the equations f(r, y,P. q) = 0 and g(r, Y.P. q) = 0 are compatible if %3D %3D a(f,g)…

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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: Let r = xi + yj + zk and r = |rl. If F = find div(F). (Enter your answer in terms of r and p.) p'…

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Q: Let f(x, y) = vax?y? + by. Compute f,(c, d) for the following values: a = 9, b = 3, c =3, d = 2.…

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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:…

Q: Let f(x.y) = In (x³y) . If f(6,2)=f,(5,a) what is the value of a? O a 1 O b. -1 Oc. 0 Od. 2 O e. -2

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