Does the function f(r,y) = e-(z²+y°) achieve an absolute minimum on D= R²? %3D

Q: dy sin x - y where f(n) = 0. dx %D |

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Q: Find the external in the isoperimetric problem of the extremum of subject to f(y² +xy'- :“)dx= 2,y…

A: Consider the functional  Iyx=∫x1x2Fx,y,y'dxwith the conditions yx1=y1 , yx2=y2and Iyx=∫x1x2Gx,y,y'dx…

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A: Minimum and maximum of a function can be calculated by testing the function against all the values…

Q: Solve the DE by Integrating Factors Found by Inspection 3 1. x dy - y dx = x¹ y dy + x³y² dx X

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Q: 27. w = ry + yz+ za, x=r cos 0, y=r sin 0, z = r0; dw dw when r = 2, 0 = 1/2 dr' de

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Q: What is the isogonal trajectories cutting at angle of 0= arctan 4 to the family of curves whose…

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Q: IND THE ORTHOGONAL TRAJECTORIES OF THECURVES Y =Cx²,WHERE CIS AN ARBITRARY CONSTANT.

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Q: Find the equation of the tangent plane to g ( x , y ) = e x cos ⁡ ( y )  at ( 0 , π ). Does g have a…

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Q: Let dy/dx =f(x, y)= x^2 -y Use Euler’s method ( with step size ℎ = 1) to approximate the value of…

A: Given, dydx=f(x,y)=x2-y y(0)=1 h=1

Q: 2ydx + x(2 + x²y) dy = 0 %3D

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Q: Solve dy / dx = 1 /( x^2 – 1) , for y(0) = 0. Find its maximal interval of existence %3D

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Q: Find a cubic function d cx bx ax x f + + + = 2 3 ) ( whose graph has a relative minimum at (0, 1)…

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Q: valuate S S Se(3 – 4x)dV, whe e xy-plane defined by 0 < x s

A: To find: ∫∫∫E(3-4x) dV

Q: Find the solution asked using the process of Homogeneous. (16x + 5y)dx + (3x + y)dy = 0; the curve…

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Q: Use Euler's method to estimate y(0.02) ey-x y' 1 + e²y ,y(0) = 4

A: Given differential equation is y'=ey-x1+e2y with the initial condition  y0=4 and step size is…

Q: = y – 2², dt dy = y - ar. - у — dt For parameter a, classify the equilibrium points when a>5

A: Both the equilibrium points (0, 0) and (a, a2) are saddles.   Explanation: Let   First, we find the…

Q: 1 in the first quadrant x>0, y>0. ху Find the minimum value of f (x, y) =x+8y+- -How do you know…

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Q: The maximum rate of change of the function f(x,y,z) = x In(yz) at (1;2;) is equal to: V17/2 None of…

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Q: 18. Find the absolute maximum and absolute minimum values for the function f (x,y) = e-**-y* (x² +…

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Q: 2. (i) Find dy where dx (а) In(ху) %3D х- у 1-x (b) 1+x dy (ii) Find the maximum value of the curve…

A: Given that  The following equations  To find the derivative

Q: 3. Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle…

A: given family of parabolas y2=cx at angle θ=60° claim- find the family of oblique trajectories that…

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

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Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation t approximate the…

A: Introduction: The linear approximation of a function at a given point is an application of…

Q: Solve using the integrating factors by inspection (y²-3-x) dy + ydx =0

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Q: Find the maximum and minimum values attained by f(x, y, z) = 2xyz on the unit ball x2 + y2 + z2 < 1.…

A: fx,y,z=2xyz on the unit ball x2+y2+z2≤1 gx,y,z=x2+y2+z2-1 ∇f=∂f∂x,∂f∂y,∂f∂z ∇g=2yz,2xz,2yx…

Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = x2 – xy + y? – 3x + 3y…

A: Determine the critical point of the function. Now determine the value of function at this point. Now…

Q: Obtain the solution using Integrating Factors Found by Inspection 1. ydx + 2(y* - х)dy %3D 0

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Q: xy' + y = sin(x), y(3) = 0, y'(3) = 0. Yh = C1x + c2x ln(x).

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Q: st, enter DNE.) f(x, y) = x² + y² + 4x 10y6 minimum maximum point (x, y, z) = (x, y, z) = (x, y, z)…

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Q: 1. Find minimum value of f (r, y) = 2x+3y-6ry on the unit square D = {(x, y) : 0 < r, y < 1}.

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Q: Find au explicit solution for the IVP. (Show work.) dy y? = 2ty", y(0) = dt 4

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Q: Eliminate the arbritrary constant/s. Show full solution. x= -In t, y= at + bt?

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Q: 1. y21 yS 4 Ax, y) = x+ y Minimum: Maximum:

A: Topic - linear programming

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

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Q: Aparticle moves on the graph of y^2=x+1 so that dx/dt=4x+4 what is dy/dt whrn x=8?

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Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: Let f(x,y)= 3+cos(x) sin(2y) a) Show that the function has a stationary point at (0,Pi/4). b) Is (0,…

A: To analyze the critical point (0,pi/4) of the given function of two variables

Q: 4 + where f(1) = -2. y : dx 业

A: If (x, f(x)) is a point where f(x) reaches a relative maximum or minimum, and if the derivative of f…

Q: Use Euler's method to approximate the solution of the IVP, yx? – 1.2y, y(0) = 1 on the interval [0,…

A: Euler's method: Euler's method is used to find the approximated solution of first order differential…

Q: Determine the critical (equilibrium) points. dy y? (6 – y²), –∞ < Yo < ∞ dt Enter your answers in…

A: Critical points are the point at which the function is 0 or undefined. First derivative is used to…

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…

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Q: f 5 J of work are needed to stretch a spring 10 cm beyond equilibrium, how much work is required to…

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Q: Find the point at which the function f(r,y) = 2 in z+2 In y attains a maximum subject to the con-…

A: Maxima or minima: For any function f(x), 1) Evaluate f'(x)=0 for critical point. 2) Evaluate f''(x)…

Q: Solve the differential eavations ydx xdy = 0 x' +y° +y?

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Q: What is the integrating factor of the linear De of order one ydx + (2 – xy)dy= 0 ?

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Q: uct Theorem. 10. K y KM=

A: Solution

Q: The longest interval in which the I.V.P y" + (tanx)y-xy x, y(1) = 3, y'(1) = 0 surlay has a solution…

A: Given,  y''+tanx y'-xy=x It is of the form,  y''+p(x) y'+q(x) y=g(x)