Question

Consider the following. f(x, y) = x/y,    P(4, 1),    u = 3 5  i + 4 5  j...

Consider the following.

f(x, y) = x/y,    P(4, 1),    u =

3
5

 i +

4
5

 j

(a) Find the gradient of f.

(b) Evaluate the gradient at the point P.

(c) Find the rate of change of f at P in the direction of the vector u.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

At first we calculate the gradient of the given function at the point (4,1). Then we find out rate of change of f (x,y) at the point p in the direction of the vector.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and ?=3?+2?v=3i+2j. A. Find the gradient of f. ∇?=∇f=  ?+i+  ?j Note: Your answers should...
Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and ?=3?+2?v=3i+2j. A. Find the gradient of f. ∇?=∇f=  ?+i+  ?j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (∇?)(?)=(∇f)(P)=  ?+i+  ?j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of ?v. ???=Duf= D. Find the maximum rate of change of f at P. E. Find the (unit) direction vector in which the maximum rate...
f(x, y, z) = xe4yz, P(1, 0, 3), u = <2/3, -1/3, 2/3> (a) Find the...
f(x, y, z) = xe4yz, P(1, 0, 3), u = <2/3, -1/3, 2/3> (a) Find the gradient of f. ∇f(x, y, z) = <   ,   ,   > (b) Evaluate the gradient at the point P. ∇f(1, 0, 3) = <   ,   ,   > (c) Find the rate of change of f at P in the direction of the vector u. Duf(1, 0, 3) =
In the following functions: a) Find the gradient of f. , b) Evaluate the gradient at...
In the following functions: a) Find the gradient of f. , b) Evaluate the gradient at point P. and c) Find the rate of change of f in P, in the direction of vector. 1- f(x. y) = 5xy^2 - 4x^3y, P( I , 2), u = ( 5/13, 12/13 ) 2- f(x, y, z) = xe^2yz , P(3, 0, 2), u = (2/3, -2/3, 1/3)
] Consider the function f : R 2 → R defined by f(x, y) = x...
] Consider the function f : R 2 → R defined by f(x, y) = x ln(x + 2y). (a) Find the gradient of f(x, y) at the point P(e/3, e/3). (b) Use the gradient to find the directional derivative of f at P(e/3, e/3) in the direction of the vector ~u = h−4, 3i. (c) Find a unit vector (based at P) pointing in the direction in which f increases most rapidly at P.
Find Duf at P f(x,y)= sin(3x-4y); P(4, 3); u=(3/5 i-4/5 j) Enter the exact answer. Duf=?
Find Duf at P f(x,y)= sin(3x-4y); P(4, 3); u=(3/5 i-4/5 j) Enter the exact answer. Duf=?
Let f(x, y) = x^2 ln(x^3 + y). (a) Find the gradient of f. (b) Find...
Let f(x, y) = x^2 ln(x^3 + y). (a) Find the gradient of f. (b) Find the direction in which the function decreases most rapidly at the point P(2, 1). (Give the direction as a unit vector.) (c) Find the directions of zero change of f at the point P(2, 1). (Give both directions as a unit vector.)
Consider the following vector field. F(x, y, z)  =  6yz ln x i  +  (3x −...
Consider the following vector field. F(x, y, z)  =  6yz ln x i  +  (3x − 7yz) j  +  xy8z3 k (a) Find the curl of F evaluated at the point (5, 1, 4). (b) Find the divergence of F evaluated at the point (5, 1, 4).
Consider the function F(x,y)=e^((-x^2/4)-(y^2/4)) and the point P(−1,1). a. Find the unit vectors that give the...
Consider the function F(x,y)=e^((-x^2/4)-(y^2/4)) and the point P(−1,1). a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find a vector that points in a direction of no change in the function at P.
For f(x, y) = x2 + 4xy - y2 at the point P(2, 1), a) find...
For f(x, y) = x2 + 4xy - y2 at the point P(2, 1), a) find the unit vector u in the direction of steepest ascent; b) find the unit vector u in the direction of steepest descent; and c) find a unit vector u that points in the direction of no change in the function. show all work please a) b) c)
Evaluate the following. f(x, y) = x + y S: r(u, v) = 5 cos(u) i...
Evaluate the following. f(x, y) = x + y S: r(u, v) = 5 cos(u) i + 5 sin(u) j + v k, 0 ≤ u ≤ π/2, 0 ≤ v ≤ 3
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT