Let d be the usual metric on R2. (a) Find d(x,y) when x = (3,−2)
and...
Let d be the usual metric on R2. (a) Find d(x,y) when x = (3,−2)
and y = (−3,1). (b) Let x = (5,−1) and y = (−3,−5). Find a point z
in R2 such that d(x,y) = d(y,z) = d(x,z). (c) Sketch Br(a) when a =
(0,0) and r = 1. The Euclidean metric is by no means the only
metric on Rn which is useful. Two more examples follow (9.2.10 and
9.2.12).
Find the maximum and minimum values of the function f(x, y, z) =
x^2 + y^2...
Find the maximum and minimum values of the function f(x, y, z) =
x^2 + y^2 + z^2 subject to the constraints x + y + z = 4 and z =
x^2 + y^2 .
part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the...
part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the partial derivatives of the function
f(x,y)=x^6y^6/x^2+y^2
fx(x,y)=
fy(x,y)=
part 3)
Find all first- and second-order partial derivatives of the
function f(x,y)=2x^2y^2−2x^2+5y
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 4)
Find all first- and second-order partial derivatives of the
function f(x,y)=9ye^(3x)
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 5)
For the function given below, find the numbers (x,y) such that
fx(x,y)=0 and fy(x,y)=0
f(x,y)=6x^2+23y^2+23xy+4x−2
Answer: x= and...
Let D be the solid region defined by D = {(x, y, z) ∈ R3; y^2...
Let D be the solid region defined by D = {(x, y, z) ∈ R3; y^2 +
z^2 + x^2 <= 1},
and V be the vector field in R3 defined by: V(x, y, z) = (y^2z +
2z^2y)i + (x^3 − 5^z)j + (z^3 + z) k.
1. Find I = (Triple integral) (3z^2 + 1)dxdydz.
2. Calculate double integral V · ndS, where n is pointing
outward the border surface of V .
Consider the function f(x, y) = xy and the domain D = {(x, y) |
x^2...
Consider the function f(x, y) = xy and the domain D = {(x, y) |
x^2 + y^2 ≤ 8}
Find all critical points & Use Lagrange multipliers to find
the absolute extrema of f on the boundary of D,which is the circle
x^2 +y^2 =8.
Find the exact extreme values of the function z = f(x, y) = x^2
+ (y-19)^2...
Find the exact extreme values of the function z = f(x, y) = x^2
+ (y-19)^2 + 70 subject to the following constraints x^2 + y^2
<= 225 Complete the following: Fmin=____at(x,y) (__,__)
Fmax=____at(x,y) (__,__)
For f(x,y)=ln(x^2−y+3). -> Find the domain
and the range of the function z=f(x,y).
-> Sketch the...
For f(x,y)=ln(x^2−y+3). -> Find the domain
and the range of the function z=f(x,y).
-> Sketch the domain, then
separately sketch three distinct level curves.
-> Find the linearization of
f(x,y) at the point
(x,y)=(4,18).
-> Use this linearization to determine the
approximate value of the function at the point (3.7,17.7).
1- find the divergence of F(x,y,z) = <e^x(y),x^2(z),xyz>
at (1,-1,3).
2- find the curl of F(x,y,z)=...
1- find the divergence of F(x,y,z) = <e^x(y),x^2(z),xyz>
at (1,-1,3).
2- find the curl of F(x,y,z)= <xyz,y^2(z),x^2(y)z^3> at
(0,-2,2)
Find the absolute maximum and minimum of the function
f(x,y,z)=x^2 −2x+y^2 −4y+z^2 +4z
on the ball...
Find the absolute maximum and minimum of the function
f(x,y,z)=x^2 −2x+y^2 −4y+z^2 +4z
on the ball of radius 4 centered at the origin (i.e., x^2 + y^2
+ z^2 ≤ 16). Lay out your work neatly and clearly show your
procedure.
Find the exact extreme values of the function z = f(x, y) =
(x-3)^2 + (y-3)^2...
Find the exact extreme values of the function z = f(x, y) =
(x-3)^2 + (y-3)^2 + 43
subject to the following constraints: 0 <= x <= 17
0 <= y <= 12
Complete the following: Fmin=____at(x,y) (__,__)
Fmax=____at(x,y) (__,__)