Consider the function f(x,y) = e^xy and closed triangular region D with vertices (2,0), (0,2) an (0,-2). Find the absolute maximum and minimum values of f on this region.
Need an explanation pls
In: Math
Find the volume of the solid enclosed by the two paraboloids y=x2+z2y=x2+z2 and y=2−x2−z2y=2−x2−z2.
In: Math
You have been asked to design a can with a volume of 500cm3 that is shaped like a right circular cylinder. The can will have a closed top. What radius r and height h, in centimeters, would minimize the amount of material needed to construct this can? Enter an exact answer.
In: Math
In: Math
A) Find the equation of the plane that passes through (2, -1,3) and is perpendicular to the line x = 2-3t, y = 3 + t, z = 5t B) Find the equation where the planes 2x-3y + z = 5 and x + y-z = 2 intersect. C) Find the distance from the point (2,3,1) to the x + y-z = 2 plane. D) Find the angle between the planes x + y + z = 1 and x-2y + 3z = 1
In: Math
Use the Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error. Check your answer graphically
X^2
In: Math
Let z=e^(x) tan y.
a. Compute the first-order partial derivatives of z.
b. Compute the second-order partial derivatives of z.
c.∗ Convert z = f(x,y) into polar coordinates and then compute the first- order partial derivatives fr and fθ by directly differentiating the com- posite function, and then using the Chain Rule.
In: Math
In: Math
A) Find a Vector Perpendicular to Vectors 2i + 3j-k and 3i + k
B) Find the area of the triangle whose vertices are (2, -1,1), (3,2,1) and (0, -1,3)
C) Find the volume of the parallelepiped with adjacent axes PQ, PR, and PS with P(1, -2.2), Q(1, -1.3), S(1,2,3)
In: Math
a.maximize and minimize −2xy on the ellipse x^2+4y^2=4
b.Determine whether or not the vector function is the gradient ∇f (x, y) of a function everywhere defined. If so, find all the functions with that gradient. (x^2+3y^2)i+(2xy+e^x)j
In: Math
A rock is thrown upward from a bridge into a river below. The function f(t)=−16t^2+36t+136 determines the height of the rock above the surface of the water (in feet) in terms of the number of seconds t since the rock was thrown.
What is the bridge's height above the water?
How many seconds after being thrown does the rock hit the water?
How many seconds after being thrown does the rock reach its maximum height above the water?
What is the rock's maximum height above the water?
In: Math
Use the Rational Zero Test to list all possible rational zeros of f. Test each possible rational zero to determine whether it is an actual zero of f. (Enter your answers as a comma-separated list. If there are no rational zeros, enter NONE.)
f(x) = x4 + 2x3 + 4x2 + 3x − 10
possible rational zeroes x=
actual rational zeroes x=
In: Math
Solve the IVP by applying the Laplace transform:y''+y=sqrt(2)*sin[sqrt(2)t]; y(0)=10, y'(0)=0
In: Math
In: Math
Compute the flux of the vector field F = <xy, 5yz, 6zx> through the portion of the plane 3x + 2y + z = 6 in the first octant with the downward orientation.
In: Math