Find the directional derivative of the function at P in the
direction of v. f(x, y)...
Find the directional derivative of the function at P in the
direction of v. f(x, y) = x3 − y3, P(8, 5), v = 2 2 (i + j)
For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a
function f(x,...
For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a
function f(x, y) such that F~ (x, y) = ∇f(x, y) = h ∂f ∂x , ∂f ∂y i
by integrating P and Q with respect to the appropriate variables
and combining answers. Then use that potential function to directly
calculate the given line integral (via the Fundamental Theorem of
Line Integrals):
a) F~ 1(x, y) = hx 2 , y2 i Z C F~ 1...
Find directional derivative of the function f(x, y, z) =
5x2 + 2xy – 3y2z at...
Find directional derivative of the function f(x, y, z) =
5x2 + 2xy – 3y2z at
P(1, 0, 1) in the direction v = i +
j – k .
. For the function f(x, y) = xye^x−y , at the point (2, 2)
(a) find...
. For the function f(x, y) = xye^x−y , at the point (2, 2)
(a) find the gradient.
(b) find the directional derivative in the direction of the
vector 3i − j.
(c) in the direction of which unit vector is the rate of
increase maximum? What is the maximum rate of increase?
(d) in the direction of which unit vector(s) is the directional
derivative zero?
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).
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...