How is the derivative of a differentiable function (x, y, z) at a point P 0 in
Question:
How is the derivative of a differentiable function ƒ(x, y, z) at a point P0 in the direction of a unit vector u related to the scalar component of (∇ƒ)P0 in the direction of u? Give reasons for your answer.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 75% (4 reviews)
Lets denote the gradient of the function xyz at the point P0 as P0 which is a vector that points in ...View the full answer
Answered By
Churchil Mino
I have been a tutor for 2 years and have experience working with students of all ages and abilities. I am comfortable working with students one-on-one or in small groups, and am able to adapt my teaching style to meet the needs of each individual. I am patient and supportive, and my goal is to help my students succeed.
I have a strong background in math and science, and have tutored students in these subjects at all levels, from elementary school to college. I have also helped students prepare for standardized tests such as the SAT and ACT. In addition to academic tutoring, I have also worked as a swim coach and a camp counselor, and have experience working with children with special needs.
0.00
0 Reviews
10+ Question Solved
Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
Question Posted:
Students also viewed these Mathematics questions
-
In Sec. 34, use expressions (13) and (14) to derive expressions (15) and (16) for |sin z|2 and |cos z|2. (13) sin z = sin x cosh y + i cos x sinh y, (14) cos z = cos x cosh y i sin x sinh y, where z...
-
Which of the following statements are true if (x, y) is differentiable at (x 0 , y 0 )? Give reasons for your answers. a. If u is a unit vector, the derivative of at (x 0 , y 0 ) in the direction of...
-
a. Give an example of a differentiable function whose first derivative is zero at some point c even though has neither a local maximum nor a local minimum at c. b. How is this consistent with...
-
Write a program that takes the name of a .wav file and a playback rate r as command-line arguments and plays the file at the given rate. First, use StdAudio.read() to read the file into an array a[]....
-
From 2012 to 2013, Berry Barn reported that its Net Sales increased from $300,000 to $400,000, and its Gross Profit increased from $90,000 to $130,000. Was the Gross Profit increase caused by (a) An...
-
While vendor discounts for early payment are very rewarding, what are some of the difficulties that may arise to keep a firm from taking advantage of those discounts? Stretching payables has often...
-
How do patrilineal patrilocal families differ from matrilineal families?
-
Jackson Ski Haus had the following statements prepared as of December 31, 2014. Additional information: 1. Dividends in the amount of $20,000 were declared and paid during 2014. 2. Depreciation...
-
1. Determine the investment portfolio composition for Kent's eastern branch that would maximize the expected effective yield while satisfying the restriction imposed by the parent. 2. What is the...
-
Sunshine Sushi, a Japanese restaurant, has the following adjusted trial balance with accounts listed in alphabetical order. Using the template provided, prepare a classified balance sheet for the...
-
Display the values of the functions in two ways: (a) By sketching the surface z = (x, y) (b) By drawing an assortment of level curves in the functions domain. Label each level curve with its function...
-
Find the partial derivative of the function with respect to each variable. h(, , ) = sin cos
-
Consider the following implementation of a class Square: public class Square { private int sideLength; private int area; public Square(int initialLength) { } side Length = initialLength; area...
-
Consider the cointegrated model Yt Xt = 0Xt + vit, Xt-1+U2t, where it and v2t are mean zero serially uncorrelated random variables with E [vtv2j] = 0 for all t and j. Derive the vector error...
-
Suppose that the daily log return of a pair of securities follows the following model: T1,t = -0.05 T2,1 = 0.1 0.1r1,-1+0.05r2,1-1 0.171,-0.3r2,1-1 + a, + a2,1 where a, denotes a bivariate normal...
-
Consider aus_airpassengers provided by the package fpp3, the total number of passengers (in millions) from Australian air carriers for the period 1970-2011. a. [2 marks] Use ARIMA () to find an...
-
Suppose you have the following panel regression equation: Yi,t = a + pYi,t-1 + i,t where Ei,t = Uit + Oui,t-1 and uit is white noise (uit is not correlated over time or across individuals). Prove...
-
(a) You want to estimate the effect of the logarithm of wages on the hours of work supplied by married women already in the workforce. The labor demand function is the second part of the system that...
-
In which of the following cases may the taxpayer claim head of household filing status? a. The taxpayer is single and maintains a household that is the principal place of abode of her infant son. b....
-
What is a manufacturing system?
-
Name a function for which the integral below represents the arc length of the function on the interval [0, 2] 2 So 1 + (4x) dx
-
Find the arc length of the graph of the function over the indicated interval. y = x 4 /8 + 1/4x 2 , [2, 3] 16 12 00 8 4 y y = 1 8 2 4x 3 4 -X
-
(a) Sketch the graph of the function, highlighting the part indicated by the given interval, (b) Write a definite integral that represents the arc length of the curve over the indicated interval and...
-
The Conference Board Economic Forecast for the US Economy August 02, 2023 | Report The Conference Board forecasts that the growth seen in many parts of the economy will gradually buckle under...
-
Project: Parole: Are We Better Off Without It? As you learned in this lesson, federal parole was eliminated in 1984. This made a dramatic impact on the incarceration system in the United States....
-
what ways does hazard analysis play a role in the design and implementation of safety instrumented systems (SIS), particularly in determining Safety Integrity Levels (SILs) and developing safety...
Study smarter with the SolutionInn App