f(x, y) = 30 for r = 0, 1,2, 3; y = 0, 1, 2, %3D Find: (a) P(X < 2, Y = 1); (b) P(X > 2, Y< 1); (c) P(X>Y ); (d) P(X+ Y = 4). 2. From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of pieces of fruit is selected. If X is the number of oranges and Y is the number of apples in th sample, find: (a) the joint probability distribution of X and Y ; (b) P[(X, Y ) E A], where A the region that is given by {(x, y) | x + y < 2}.

Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

Q: Q4. Starting from the initial trial solution (xı, x2) = (0, 0), apply the gradient search procedure…

A:

Q: Solve the given optimization problem by using substitution. Minimize S = xy+xz + yz subject to xyz =…

A:

Q: e function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant

A: The given function is f(x,y)=x-12+y-12 and subjects to the constraint x2+y2=8 the formula for the…

Q: Integrate f(x, y) = 4c®* - 0.5y using h = 0.5 with y(0) = 2 from x =0 to 0.5.

A:

Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: Perform three iterations of the steepest ascent method to locate the maximum of f(x,y) = 3.5x + 2y +…

A: Consider the given function f(x,y)=3.5x+2y+x2-x4+2xy-y2 and initial guesses as  x=0y=0

Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

A:

Q: Find fz(x,y) and fy(x, y) given f(r, y) = csc yArcsin(r²).

A:

Q: b) Data was collected on 344 corporate executives to find out the effect of MBA degree and work…

A: As per the guideline, 3 subparts can be answered. please repost the remaining subpasrts. thank you.

Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: 2. Use the method of Lagrange multipliers to show that for x, y ≥ 0, we have z"+"> (²+)" 2

A: Introduction: For minimizing a multi-variable function under some certain constraint or constraints,…

Q: Find fzyx. 8.8 f(x, y, z) = x*y°z® +xy³ + y°z f zyz ||

A: GIVEN: f(x, y, z) = x4 y8 z8 + xy5 + y5 z

Q: valuate S. F · ds, where F(x, y, z) = (z, x, y) and c(t) = (t, t², t³), 0 < t < 1.

A: F(x,y,z)=(z,x,y)

Q: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: Q3\ Solve the problem minimize * J[y]= [[v +y"- 2y dx ,subject to the conditions y (0) =1 and y(1) =…

A:

Q: 2. A cafe estimates a monthly profit (in thousand pesos) of P(x, y) = 27 – x? – y² + 6y if they open…

A: Given: A cafe estimates a monthly profit, P(x, y)=27-x2-y2+6y and the region D=x, y∈ℝ2 : x2≤y≤4. To…

Q: A small blood vessel of radius r branches off at an angle θ from a larger vessel of radius R to…

A:

Q: Given f (x,y) =5x2+ 3x²y²+4y2, match the partial derivative with the expression on the right. v df…

A:

Q: Find the relative maximum and minimum values. f(x,y) = 3x² – 4y?

A:

Q: Compute fe F d where F (x, y) = x² + y). (2xy + x, Hint: Is F conservative?

A:

Q: 3. Evaluate f 2xdx + (y + 2)dy along the rectangle with vertices (0, 0), (0,3), (3,3) and (0, 3).

A:

Q: A cafe estimates a monthly profit (in thousand pesos) of P(x, y) = 27 – x² – y? + 6y if they open a…

A:

Q: Find a slope of the solution of y' = t – y at (3,1).

A: We have been given a linear differential equation dydt=t−y ______(i) (As y′=dydt)We have to find the…

Q: Find fr, fy and fz. f(x, y, z) = x – Vy² + z? |

A: Given f(x,y,z)=x-y2+z2. The objective is to find fx,fy and fz.

Q: Integrate f(x, y) = y(x² + y³) 3 over the domain x² + y° 0.

A: Given function is fx,y=yx2+y23 and domain is x2+y2≤4 with y≥0 We have to integrate fx,y=yx2+y23 over…

Q: B. Find the indicated partial derivatives: af af 7. fls.y) = cn{«-y?), y

A:

Q: f(x, y, z) = e-3zyz 三 fy = 三 ニ f.

A:

Q: Find fr and fy- f (x, y): 6e dt 4 fa(x, y) = fy(x, y) =

A:

Q: (a) Find the critical point of f(r, y) = (4x² – 3) (2² + 43y). (x, y) (b) Find the discriminant,…

A:

Q: ||| V3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8.

A:

Q: Find the particular sölution f"(x) = 4, f'(2) = 12, f(2) = 17

A: integration 2 times and after applying initial condition we get f(x)

Q: Find the partial derivative. 3p f (p, q) = e af

A:

Q: Use the Chain Rule to calculate the partial derivatives д(т, у) — sin (т? + у?), х— 4и — v, у — —…

A: Given g(x, y)=sin(x2+y2) ,x= 4u-v and y=-(2u+2v)

Q: [2xy + yz (i) F(x,y, z) = x2 + xz with domain R³. || xY

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

Q: By utilizing Gradient Descent where initial x1=x2=Dx3%3D0, What is the approximated min. point of…

A: To find - By utilizing Gradient Descent where initial x1 = x2 = x3 = 0, What is the approximated…

Q: Find fr and fy- f (x, y) = | 5e dt %3| fa(x, y) = fy(x, y) =

A: We apply fundamental theorem of calculas and solve it.

Q: 4x 28. If R = and errors in x, y, z be 0-001. Show that the maximum relative error at x = y = z = 1…

A:

Q: Use the Chain Rule to evaluate the partial derivative at the point specified. ag at s = 9, where…

A:

Q: Find the four second partial derivatives. z = 6x2 + y5 a2z дхду дудх ду?

A: We will find all the asked second order partial derivatives as following.

Q: (c) Suppose that two of the pipes become blocked so that x3 = 0 and x1 = 0. Determine the flow rates…

A: Topic - flow diagram

Q: C(x) = 1500 + 13x – 0.1x2 + 0.0005x3. - %3D Find the marginal inal cost finctien?

A: Given query is to find the marginal cost function.

Q: 2. Find the linear approximation of f(x) vx at x 4. Then, find the approximate value of 4.4 using…

A:

Q: Find all values of x and y such that fx = 0 and fy = 0 simultaneously. 13. f(x,y) = e*»+y?

A:

Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

A:

Q: © f(X,y) = x4 + 'onY -10 © w = x*y - 10yZ z³ + 43X – 7tan (4Y)

A: It is partial derivative