Explanation Given information: Thesurface z 2 − 2 x 4 − y 4 = 16 , and point P = ( 2 , 2 , 8 ) Formula used: The normal vector to a surface f ( x , y , z ) is n ^ = ∇ f ‖ ∇ f ‖ , where ∇ f = ( f x , f y , f z ) is gradient of f ( x , y , z ) Calculation: As surface is given z 2 − 2 x 4 − y 4 = 16 , thus f ( x , y , z ) = z 2 − 2 x 4 − y 4 − 16 = 0 , thus to find unit normal vector on it First find its gradient, thus ∇ f = ( f x , f y , f z ) = ( ∂ f ∂ x , ∂ f ∂ y , ∂ f ∂ z ) = ( ∂ ( z 2 − 2 x 4 − y 4 − 16 ) ∂ x , ∂ ∂ y ( z 2 −

4th Edition

ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 14.5, Problem 61E

To determine

Find unit n normal vector to the surface z2−2x4−y4=16, at P=(2,2,8) in direction of xy- plane

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.5, Problem 60E

Chapter 14.5, Problem 62E

Students have asked these similar questions

Find the general solution to the differential equation

charity savings Budget for May travel food Peter earned $700 during May. The graph shows how the money was used. What fraction was clothes? O Search Submit clothes leisure

Exercise 11.3 A slope field is given for the equation y' = 4y+4. (a) Sketch the particular solution that corresponds to y(0) = −2 (b) Find the constant solution (c) For what initial conditions y(0) is the solution increasing? (d) For what initial conditions y(0) is the solution decreasing? (e) Verify these results using only the differential equation y' = 4y+4.

Chapter 14 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

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.

Find unit n normal vector to the surface z 2 − 2 x 4 − y 4 = 16 , at P = ( 2 , 2 , 8 ) in direction of xy- plane

Solution Summary: The author calculates that the normal vector to a surface is f(x,y,z).

Concept explainers

Videos

Find unit n normal vector to the surface z2−2x4−y4=16, at P=(2,2,8) in direction of xy- plane

Want to see the full answer?

Chapter 14 Solutions