Find the mioimum and maximum values of the function subject to the gicen fCx.y)=6x?+Sy? 3X+10y=3

Q: M is the midpoint of AB 2x + 1 and MB AM = %3D 1 ond AM

A: Given;- M is the mid point of AB AM=2x+1 and MB=3x-2    Therefore, AM=MB 2x+1=3x-2 3x-2x=1+2 x=3

Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

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Q: Solve the problem in an unknown interval z E [0, a] using transversality condition J = min y(1),a.…

A: Solution:-

Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D x² +x – 6' has a…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,∂f∂y=0,…

Q: At what interval is y=x^3-3/2x^2 concave upward?

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Q: Find the family of oblique trajectories that intersect the family of the paraboles y = Cx at angle e…

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Q: Q1 Find thr relative maximum and minimum of: fx, y) = x² + y² + z?given that 9x? + 4 y² + 2z? = 36…

A: Consider the provided question,  minimize and maximize, fx,y,z=x2+y2+z2                        ....1…

Q: Suppose z is a function of x and y, and csc Vx2 + yz = 2"esin . Solve for dz and ду

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Q: Find a solution of x dy =y?-y that pases du Through indicated points

A: For the given problem, below is the solution.

Q: 3. Describe the level surfaces of the function. f(x, y, 2) = x² + 4y? + 42?

A: We Know that,  A level surface of a function w = f(x, y, z) with three variables is a surface f(x,…

Q: Find the exact length of the curve. y= In{1 – x²), o s 1. 0 sxs! 7. I Ju =

A: We will find the exact length of the curve as shown below

Q: use the trapezoidal rule to approximate use n=6 and h=1

A:

Q: Find the extremum of f(x,y) = 9x2y² +4y² + 4x². %3D Answer:

A: Topic= Derivative the extremum is 0.

Q: For what minimum integer value of a, will the line ax+(a+1) y =18 www (a> 0) have two intersection…

A: If the line cuts the circle at two points then given line is secant line of the circle .The…

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle = 13. 5. x² + y

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Q: 4. The square STUV has diagonals that intersect at point W, where SU = 4x + 26 and TW = 8x- 41. Find…

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Q: Determine the convexity/concavity property of the following: (ii) f (x, y) = 2x² – y?

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Q: Show that the square of the length of the subtangent at any point on the curve by2=(x+a)3 (b is not…

A:

Q: Solve the following CDES by variation of paramete y" + 5y' + 4y = x²e²x

A: The given equation is y''+5y'+4y=x2e2x The auxiliary equation is…

Q: Show that the minimum distance from the origin to a point on theplane ax + by + cz = d is

A: Given: ax+by+cz=d we know that minimum distance p of a point x1,y1,z1 from given equation of plane…

Q: Find the extremum of f(x,y) = 3x²y² +5y² + 5x?. Answer:

A: Given:- f(x, y) = 3x2y2+5y2+5x2 To find:- Extremum of f(x, y)

Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: Show that the maximum value of f (x, y) = x 2 y3 on the unit circle is

A: We should maximize f(x,y)=x2y3 under the constraint gx,y=x2+y2 where x2+y2=1. Now, ∇f=2xy3,…

Q: Find the best quadratic approximation, Q(x, y) of V9 – 6x – 4y for (r, y) near (0,0).

A: We have to find the best quadratic approximation Q(x,y) for (x,y) near (0,0).

Q: Find the values of the constants a, b, c so that F = (axy + bz3)i+ (3x² – cz)j + (3xz? – y)k Is…

A: A vector F→ is said to be irrational if and only if cure F→ =0 i.e∆ x F→ = 0Given F→ = (axy+bz3) i^…

Q: Find the extreme values of g(x,y,z) = 2x² + xy + 4y² + xz + z² + 2. %3D and determine whether the…

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Q: where Projuct of in tegra tion SÃr dR A-zi-xj-YK and =dxi +arj +dzK dR and %3D the seguent of the…

A: Use line integral

Q: Find the extremum of f(x,y) = 7x²y2 +4y2 4x2. Answer:

A:

Q: Show that the function f(x, y) = (y + ax)²ev+a satisfies the equation given by %3D a2

A: Please see the explanation below....

Q: Find the length of one branch of the curve ay? = x3 from x = 0 and x = 5a. 4.

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Q: Find the maximum and minimum values of the function f(r, y) = 10 + 5x + 14x2 + 8y + 14y? on the disk…

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Q: Find the extremum of f(x,y) = 5x²y² +5y² + 6x?. Answer:

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Q: The x, y, zER, subject to the condition yz + zr + xy = 12. Then greatest value of rvzis (a) 6 (b) 8…

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Q: Find the point on the parabola x = t, y = t²,-∞ < t < ∞o, closest to the point (2, 1/2). (Hint:…

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Q: If VT bisects ZSTU, solve for x. T 3x + 2 12 U V 33

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Q: Find the length of the parabola given by c(t) = (t, t2) for 0 ≤ t ≤ 1.

A:

Q: Show that the square of the length of subtangent at any point on the curve by =(x+a)°.(b÷0) varies…

A: We will prove it as following.

Q: Determine to and the Values of sake following y PDES elliptic, parabolik, or J hyperbelic tho + X…

A: Let us consider the PDE of the form a∂2ϕ∂x2+b∂2ϕ∂x∂y+c∂2ϕ∂y2=0. Determine ∆=b2-ac. The PDE is…

Q: Find the extremum of f(x,y) = 5x²y² +4y² + 6x². %3D Answer:

A: The given function is f(x,y)=5x2y2+4y2+6x2 .......................... (1)

Q: Find the extremum of f(x,y) = 4x²y2 +3y? + 5x?. %3D Answer:

A:

Q: Find the minimum and maximum values of f(x,v) = x2 - 3y + y³, x² +4y? < 36

A: Given,         f(x,y)=x2-3y+y3  and   x2+4y2≤36.

Q: graph the points z = x + iy that satisfy the given conditions. 5. a. |z | = 2 6. | z - 1| = 2 7. |z…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle e…

A: The answer is given below:

Q: y = In(1 – a²) ; 0 < æs

A: Solution:-

Q: If Jf(x)dx = cotx? +C, then f(x) is equal to

A: ∫f(x)dx=cot x2+C

Q: The formula for the midpoint of (x1, y1) and (x2, Y2) is: M =| O True O False

A: