Explanation Given information: ∇ f = ( x , y 2 , z 3 ) Formula used: Gradient of a function f ( x , y , z ) is ∇ f = ( f x , f y , f z ) The integral formula ∫ x n d x = x n + 1 n + 1 Calculation: To find function f ( x , y , z ) such that ∇ f = ( x , y 2 , z 3 ) , comparing this with the formula ∇ f = ( f x , f y , f z ) We have, f x = x , f y = y 2 & f z = z 3 From f x = x we have f x = x ⇒ d f d x = x ⇒ f = ∫ x d x ⇒ f = ( x 2 2 ) + C 1 ( y , z ) = x 2 2 + C 1 ( y , z )

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

See similar textbooks

Videos

Question

Chapter 14.5, Problem 54E

To determine

To find function f(x,y,z) such that ∇f is a vector (x,y2,z3)

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.5, Problem 53E

Chapter 14.5, Problem 55E

Students have asked these similar questions

Explain the key points and reasons for 12.8.2 (1) and 12.8.2 (2)

Q1: A slider in a machine moves along a fixed straight rod. Its distance x cm along the rod is given below for various values of the time. Find the velocity and acceleration of the slider when t = 0.3 seconds. t(seconds) x(cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 30.13 31.62 32.87 33.64 33.95 33.81 33.24 Q2: Using the Runge-Kutta method of fourth order, solve for y atr = 1.2, From dy_2xy +et = dx x²+xc* Take h=0.2. given x = 1, y = 0 Q3:Approximate the solution of the following equation using finite difference method. ly -(1-y= y = x), y(1) = 2 and y(3) = −1 On the interval (1≤x≤3).(taking h=0.5).

Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

Chapter 14 Solutions

Calculus: Early Transcendentals

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

Knowledge Booster

$Calculus$

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.

To find function f ( x , y , z ) such that ∇ f is a vector ( x , y 2 , z 3 )

Solution Summary: The author explains how to find the function f(x,y,z) by comparing it with the integral formula.

Videos

To find function f(x,y,z) such that ∇f is a vector (x,y2,z3)

Want to see the full answer?

Chapter 14 Solutions