Given a quadric surface in the xyz-space with equation
ax2 + by2 + cz2 = d,...
Given a quadric surface in the xyz-space with equation
ax2 + by2 + cz2 = d, where a, b, c, d are real constants, that
passes through the points (1,1,−1), (1,3,3) and (−2,0,2), find a
formula for the quadric surface.
Let S1 be the level surface given by the equation f(x,y,z)
=k1and letS2be the level surface given by the equation g(x,y,z)
=k2. Suppose that C is the curve of intersection of the
surfacesS1andS2andassume that P is a point on C. show that any
tangent vector to C at P must be parallel to∇f(P)×∇g(P)
The market demand for gym memberships in North Florida is given
by the equation
Q D N = 1000 − 20 p,
and the market demand for gym memberships in South Florida is
given by the equation
Q D S = 1200 − 40 p.
Price is measured as the monthly membership fee and quantity is
measured as memberships per month. In this problem assume North
Florida and South Florida are separate and independent markets.
(a) Suppose the membership fee...
Assume that the market demand curve for pesticides is
given by the following equation: P(D) = 1000 − 2Q(D), and the
market supply curve, which is equal to the aggregated marginal cost
curve of all producers, is given by, P(S) = 200 + 2Q(S). Pesticide
production, however, is associated with harmful side effects on
both workers and nearby households and firms. The total damage to
the surroundings is proportional to output according to: SMC= 250 +
2Q.
a) Without any...
1(i) Show, if (X, d) is a metric space, then d∗ : X × X → [0,∞)
defined by d∗(x, y) = d(x, y) /1 + d(x, y) is a metric on X. Feel
free to use the fact: if a, b are nonnegative real numbers and a ≤
b, then a/1+a ≤ b/1+b .
1(ii) Suppose A ⊂ B ⊂ R. Show, if A is not empty and B is
bounded below, then both inf(A) and inf(B) exist and...
Multivariable Calculus: Surface Area and Change of Variables
Find the surface area of the surface given by z
=18−2x−3y over the triangle with vertices: (0,0), (2,3), (4,1).
Since this is not a type I or type II region, you will either need
to divide the region into two regions or use a change of variables.
x=(1/5)(u-2v) and y=(1/10)(3u-v) is a possible change of
variables.
I will upvote answers!
Given f(x) = ax2 + k (where f(x) is a quadratic),
describe when its reciprocal function would and would not have
vertical asymptotes. Refer to the values (+,-,0) of a and k in your
description. What are all the possible scenarios?
Given the surface x= (3 (y-1)^2)+ (2 (z+ 3)^2)+ 7. Find an
equation of the tangent plane at the point(12,2,2) in four
ways:
a) By using the surface as given,x=h(y,z)
b) By writing the surface as z=f(x,y)(only keep the square root
whose sign corresponds to the point(12,2,2)).
c) By writing the surface as y=g(x,z)(only keep the square root
whose sign corresponds to the point(12,2,2)).
1a.Find the equation of the tangent plane to the surface √ x +
√y + √ z = 4 at P(1, 1, 4).
1b.Let f be a function of x and y such that fx = 3x − 5y and fy
= 2y − 5x, which of the following is always TRUE?
a. (0, 0) is not a critical point of f.
b. f has a local minimum at (0, 0)
c. f has a local maximum at (0, 0)...