7a please SM 7. Consider the problem min x? - 2x + 1 + y2 - 2y s.t. (x + y) x +y + b = 2/a where a and b are positiv...
-y-2x 2+2y de If - 1 + xy + y2 + x2 = 0 and it is known that day find all coordinate points on the curve where x = -1 and the line tangent to the curve is horizontal, or state that no such points exist.
1. Solve the following differential equations: a. xy'=y+Vxy x+2y+3 y'= b. 2x – y +5 x+2y+3 y'= x+2y+5 y cos(x+y)+x+y d. sin(x + y) + y cos(x+y)+x+y C. y'=
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Problem 1 (weight 25%) Consider the problem Maximise f(x, y, z) = x + y +2z when g(x,y,z) = x2 +y2 +2z2 = 4. (*) (a) Explain why the problem (*) does have a solution (b) Suppose that ( has a solution, and use Lagrange's method to set up the necessary conditions for solving the problem. (c)Find all the triplets (r. y, 2) that satisfy the necessary conditions for solving the problem (*),...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Use the reduction of order method to solve the following problem given one of the solution y1. (a) (x^2 - 1)y'' -2xy' +2y = 0 ,y1=x (b) (2x+1)y''-4(x+1)y'+4y=0 ,y1=e^2x (c) (x^2-2x+2)y'' - x^2 y'+x^2 y =0, y1=x (d) Prove that if 1+p+q=0 than y=e^x is a solution of y''+p(x)y'+q(x)y=0, use this fact to solve (x-1)y'' - xy' +y =0
Solve the separable initial value problem. tan(sin(x^(2) 1. y' = 2x cos(x2)(1 + y2), y(0) = 5 → y= 2. v' = 8e4x(1 + y2), y(0) = 2 + y=
Please answer #2 A and B for the Lightbulb problem
"dy", etc. (a). The marginal density, fr (y), of Y. (Be explicit about all cases.) (b). P(X > 0.1 IY 0.5) (c), E(X | Y 0.5) 2x +2y ) dy 3y: if 0 y < 1, and 0 otherwise 0.1 r2x +2 (0.5) (3) 0.5 dx 64/75 2x +2(0.5) (3)0.52 dx- 5/18 2. Let Y be the lifetime, in minutes, of a lightbulb. Assume that the lightbulb has an expected...
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Show that F= + X0, +99, + (x+y). (where Problem 1. V -0) satisfies the equation v'(V°F) - 0 videnotes the operator ax ay? Problem 2. Given: Eu - (1-0) ReZ-(1 +vby Im Z Ev - 2 Im Z - (1 +) y Re Z Show that these expressions for the displacements, u and y, are consistent with Hooke's law equations. (Plane stress): Ex -0,-voy E, -, -vo E_Y = ? 2(1+0) Problem 3. For a...
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Compute wise (Hint: use the FT of line integrals. We could not use it for the circle centered at the origin, but we can use the theorem for this circle. Why?) (b) Let 0 be the angle in polar coordinates for a point (x, y). Check that 0 is a potential function for F
3. Consider the...
Problem 81 Find the point farthest from (1,3,-1) such that x2 + y2 + z2-11 and x-y+z < 3. What happens to the maximum distance if the 11 on the right side of the inequality is perturbed? 81. Suggestions (a) Take as objective the square of the distance from (x, y, z) to the point given (b) For the case of points inside the given sphere and with x-y+ z = 3, you might solve the Lagrange equations for x,...