(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. f(x, y) = x/y, P(2, 1), u=i+i + j%3|f(x, y) = x² In y, P(3, 1), u= -i+ Bj= (0. §. – })<금, 음, 몸)f(x, y, 2) — х'уг — хуз", Р(2, —1, 1), и%—uf(x, y, г) — у'е", P(), 1, — 1), и%313 13, 13

"Since you have asked multiple questions, we will solve the first question for you. If you want any…

Answered: f(x, у) — х/у, Р(2, 1), и %3D i +j

Math

Calculus

f(x, у) — х/у, Р(2, 1), и %3D i +j

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 30E

See similar textbooks

Related questions

Q: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

Q: 8 f(x, y) = y/x, P(1,2), u = }(2i + 5 j) |(2i + /5 j)

A: To find the gradient at the given point and then rate of change for the given function.

Q: consider the function f(x, y) = esin(z) y Evaluate the gradient at the point (, 1) 6

Q: (10) Given: f (x, y, z) = %3D 2y-z a) Find the gradient of f (x, y, z). b) Find the derivative of f…

A: (a) Given function is fx, y, z=x2y-z. The gradient of a function is defined as follows: ∇fx, y,…

Question

(a) Find the gradient of f.

(b) Evaluate the gradient at the point P.

f(x, y) = x/y, P(2, 1), u=i+
i + j
%3|
f(x, y) = x² In y, P(3, 1), u= -i+ Bj
= (0. §. – })
<금, 음, 몸)
f(x, y, 2) — х'уг — хуз", Р(2, —1, 1), и%—
u
f(x, y, г) — у'е", P(), 1, — 1), и%3
13 13, 13

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 18 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differentiation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Find f„(x, y). f,(x, y), Sa( – 2, 4), and f,(4, - 3). 5. fх, у) 3D 2х —-5ху 6. f(x, y) = 5x + 7y
Find f,(2, 4) and f,(2, 4) for f(x, y) = x* + 4x?y³ + 8y*. 2.3 f-(2, 4) = f,(2, 4) =
Vy + z f(x, у, 2) 3 (а) f(1, 5, 4) (b) f(6, 7, –2)
The equations ry? + 5xzcos(u) + ye" = 10 and x³yz + xe" – 10u2v² = 30 are solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v) %3D (풍,0). Find (을),y at P. du Türkçe: zy? + 5æzcos(u) + ye" = 10 ve r³yz + xe" – 10u²v² = 30 denklemleri P noktası (x.y,z)=(1,1,1) ve (u, v) = (5,0) civarında xy ve z'nin fonksiyonu olmak üzere u ve v için çözümlü olsun. P'de ()2y yi hesaplayınız.) du dz -25,00 O 80,00 10,00 O - 100,00 -0,20
If f.(x, y) = 13x + 8y + 11, || f.(3, 2) = a. b. f„(5, 2)
Evaluate af да (a,b)=(0,0) given that f(x, y) = 3x² + [y]; x = e²a+b; y = a² + t² +1
(4-.1.P)an (4-t,t,) and V(t) = (3, t,
(x2y-)水 + (2x +y+) dy~ 0 let メーuー1, dx = du yov-l, dy ody LINE 1 %3D LINE 2 (4-1+ 2y - 2-1) du t (2u-2+ v -I+1) dy =0 (u+ 2x) du + (2u + v) dy レINE 3 LINE 4 ミO let u= 2y du こ 2dy + yd2 レINE S LINE 6 (ZY + 2Y)(zdvt ydz) + (22y +y)dx =0 LINE 8 (2+2)( zdv + vdz) + (22 t1) dy = 0 LINE 7 ○=Xp(人+人そ2 LINE 9 (22+ 2え)d +(22+1)d+ (2+2) vd2= 0 Qコ入や(1+ぞて +P^(て+そ) + Pモ (て十そ) LINE 10 %3D (2²+ 27 t 1) av + (2+2)ydz =0 2+2-dz 22+42 + In (x) + Y2 In (22t 42+1) = C LIANE 14 In (vZ) + In (2²+ 4z+) =C In Lv (22 +42 +1]-'C LINE II LINE 12 LINE 13 LINE IS LINE Ib ye (z-+42+)こC v2 (Wん + 4u +)=C u2 + 4uy t yZ LINE 7 LINE 18 LINE 19 v( 42 + 4uY+x2=C (メ)2+4[xtり(リー)+ (yー)2-C レINE 20 LINE 21 %3D
W(s, t) = F(u(s, t), v(s, t)), where F, u, and u are differentiable. If u(-6,0) = 6, u,(-6,0) = -2, u(-6,0) = 2, v(-6,0) = -8, v.(-6,0) = 8, v(-6,0) = -9, F.(6,-8)= 5, and F.(6,-8)= -7, then find the following: W.(-6,0) = W₁(-6,0) = Submit Question
Calculate af Әх af af af ах ду' Әх af ?x af ду (1, -1) af ду (1, -1) (1, -1) f(x, y) = x4y3 - х = = , and = af ду when defined. (If an answer is undefined, enter UNDEFINED.) (1, -1)
If F(u,v) = (u-v) / (u+v), Find F + F (u, v)
Vx (-y +2,22 +323, 2233) =? 0 (3y -3222, 223, -2 + 2) 0 (-3y +3X372, -332, 1 + 2x) 0 (2y +2224-423,1 + 22) 0 (-34-3222, 42,1 +22) 0 (-3y +322y2, -3'2, 1 + 2)