Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

Q: 3. Find (6-+- vē)dt Vy 4. Find S- dy (4-yの?

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

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Q: The integrating factor of the LDE y' = x - 2ycotx is

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Q: 16. Of all points (x, y, z) that satisfy 3x + 4y + 2z = 52, find the one that minimizes (x – 1)2 +…

A: Let f(x,y,z)=x−12+y−42+z−22   and    g(x,y,z)=3x+4y+2z−52≡0Apply Lagrange Multiplier method to find…

Q: Let y= 3x2 +7x+4. If Δx=0.4 at x=2, use linear approximation to estimate ΔyΔy

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Q: (a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of…

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Q: Find the absolute maximum and minimum values of the function f(x, y) =2x2− 4x + 3y2 + 2 on the…

A: Given f(x,y)=2x2-4x+3y2+2           R=x,y:(x-1)2+y2≤1let g(x,y)=(x-1)2+y2-1and let F(x,y) = f(x,y)=…

Q: Let f(x, y) = 3x² – x – 3y + 5y2 – 10xy. - - - List the critical point:

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Q: 5. Deduce the standard linear approximation of 1 x2+y2+z2 at Po(1,2,3).

A: The general formula of the standard linear approximation for f(x,y,z) is generally given by,…

Q: Expand x'y + 3y - 4 about the point (1, -2) by Taylor' s theorem.

A: Let, the given function be fx,y=x2y+3y-4 and the given point is 1,-2

Q: Q4/ 1- Evaluate: f/2fy sinx dy dx ди 2- If u = x² + ey² ,x= sin 2t , y = cost² find at

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Q: Minimize S = xy + xz + yz subject to xyz = 3 v

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Q: 3. Integration by parts: 3x d x (V3 2x+4

A: To find out the integration.

Q: Find the least squares quadratic which best fits the curve Y= ex interval •< X<I ao+aix +azx over…

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Q: 8) Find the family Coff esponding to of orthogonal trajectories y=kx".

A: To find the orthogonal trajectories corresponding to below curve.

Q: 7. what is the durivative oF q= arc cSc V1-3X %3D 3 Cz -Gx)I- 7 X 3. C2-6x)1-3x (-3x)-3x 3 C1- 3x)-3

A: First make it in simple trigonometric functions then diffrenciate it and just put all the given…

Q: x, y≥0 Corner points at ________________

A: The equations given are, 2x+4y≥8  4x+3y≥12  x, y≥0 To minimize , T=x+3y+10. First obtain the corner…

Q: 11. Find the length of the curve x = on the interval [2, 4] (integrate with respect to y) 12y3

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Q: x³y³dy у2— 4у-21 (x – x4y)dy + (y + x³y²)dx :

A: See the solution and follow the step.

Q: Let y=2x^2+3x+3. If Δx=0.1 at x=4, use linear approximation to estimate Δy Δy≈

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Q: (3) Integrate using an appropriate substitution 2e- -d.xc e + 3 x-

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Q: A manufacturer incurs the following costs in producing x water ski vests in one day, for 0<x< 175:…

A: Given : The manufacturing cost of x vest in one day is given by  C (x) = 0.05 x2 + 25 x + 500 ,…

Q: 3. Find the solution of xydx – (x²+2y²)dy = 0. Use Determination of Integrating Factors.

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Q: 16. Let y = 4x² + 7x + 4. If Ax = 0.2 at x = 2, use linear approximation to estimate 4y Ay 2

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Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

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Q: Integrate  zex^2 + y^2  over the cylinder  x2 + y2 ≤ 25, 2 ≤ z ≤ 5.

A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

Q: i need help to solve this: y''+ 5y' + 6y = δ(t-2) intial conditions: y(0)=0 ,  y'(0) = 1

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Q: 2. Use the 4th-order Runge-Kutta method to integrate dx = t - sinx dt given x(0) = 1, using a step…

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Q: Give the family of orthogonal trajectories of y^2=Cx^5+5.

A: To find →Family of orthogonal trajectories of y2=cx2+5 -1

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: find the general solution using integrating factor method  dy/dy - y/2 = 2sin(3t

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Q: 4 to Use the Trapezoidal Rule with n = 1 approximate J-1 V1-x³

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Q: (tiy t 3y" -x)dn + x (x+ Jdy = 0 2

A: Given differential equation is  4xy+3y2-xdx+xx+2ydy=0 find the general solution of the given DE

Q: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: x² + y² F(x, y) =- - is a homogeneous function of degree

A: For finding degree of homogeneous function, Put x=hx and y=hy

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

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Q: tion of the separable equation dy 23 3 +2)³ + 2)?

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Q: (x In 2x dx = u v- Jv du -Svdu- Using Integration By Parts, Fand uv- fvds uv- Jvau 3 3 xVX In 2x-V지…

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Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

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Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: Let y=2x^2+7x+4. If Δx=0.3 at x=5, use a linear approximation to estimate Δy. Δy≈ ?

A: y=2x2+7x+4, ∆x=0.3 &amp; x=5 Differentiating with respect to x, we get dydx=22x+71+0=4x+7 Now at…

Q: hich vect וdtiolו y and 2? 1 -2 y = 1 -6 x = 2 8 -1 2 -1 5 2 -3 [ 2 -1

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Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: Find X1 & X2 using Newton's method to minimize x2 – y2/2 starting from (1,1)

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Q: SOLVE FOR THE ORTHOGONAL TRAJECTORIES X'(3k-x) - ky = xy

A: Take first derivative and eliminate k.

Q: 3. Integrate! 12e-0.21 а) -dt b) 6r 3,2 Se041 dr dx c) f- x. V1+ In 3x?

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Q: 2. Reverse the order of integration of S Saz dxdy. y+2

A: The objective is to reverse the order of integration

Q: a.) What is the average cost C(x) per vest if x vests are produced in one​ day?   b.) Find the…

A: The average of a function over a specified interval is the integral of the function on that interval…

Q: Find two numbers x and y with x-y = 20 for which the term xy is minimized.

A: In this problem, we have to find the two numbers "x and y"

Q: I Sdve for dydx using the four-step rule 2. Y = x- x 2.

A: