Question

find all solutions to x^2+y^2=2z^2

Answer #1

please upvote

find all solutions e^(2z) = -4i

Is the set of all x, y, z such x+ 3y + 2z = 0 a subspace of R^3
? If so find a basis for the space.

Find all solutions to the differential equations.
(a) x^2 yy' = (y^2 − 1)^(3/2)
(b) y' = 6xe^(x−y)
(c) y' = (2x − 1)(y + 1)
(d) (y^2 − 1) dy/dx = 4xy^2
Leave your answer as an implicit solution

Find the angle between the plane x+y+ 2z = 6 and the line x-1 =
y-3 = z+2

Find a fundamental set of solutions of x^2 y"-2 x y' + (x^2 +2)
y = 0 , given that y = x sin x satisfies the
complementary equation

For f(x,y,z) = sqrt(35-x^2-4y^2-2z) 1. Find the gradient of
f(x,y,z) 2. Evaluate delta f(x,y,z) 3. Find the unit vectors U+ and
U- , that give the direction of steepest ascent and the steepest
descent respectively.

Find an equation of the plane perpendicular to x+y−2z = 1 and that
contains the intersection of x − z = 10 and y + 2z =
11.

Find all solutions to the following systems. Express answers as
ordered pairs. x^2+y^2=7x+24 ,2x=y^2

Find the maximum and minimum values of the function
f(x,y,z)=3x−y−3 subject to the constraints x^2+2z^2=324 and
x+y−z=−6 . Maximum value is , occuring at ( , , ). Minimum value is
, occuring at ( , , ).

3. Consider the differential equation: x dy/dx = y^2 − y
(a) Find all solutions to the differential equation.
(b) Find the solution that contains the point (−1,1)
(c) Find the solution that contains the point (−2,0)
(d) Find the solution that contains the point (1/2,1/2)
(e) Find the solution that contains the point (2,1/4)

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