Explanation Given information: The surface 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

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

See similar textbooks

Videos

Question

Chapter 14.5, Problem 60E

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 59E

Chapter 14.5, Problem 61E

Students have asked these similar questions

Suppose an oil spill covers a circular area and the radius, r, increases according to the graph shown below where t represents the number of minutes since the spill was first observed. Radius (feet) 80 70 60 50 40 30 20 10 0 r 0 10 20 30 40 50 60 70 80 90 Time (minutes) (a) How large is the circular area of the spill 30 minutes after it was first observed? Give your answer in terms of π. square feet (b) If the cost to clean the oil spill is proportional to the square of the diameter of the spill, express the cost, C, as a function of the radius of the spill, r. Use a lower case k as the proportionality constant. C(r) = (c) Which of the following expressions could be used to represent the amount of time it took for the radius of the spill to increase from 20 feet to 60 feet? r(60) - r(20) Or¹(80-30) r(80) - r(30) r-1(80) - r−1(30) r-1(60) - r¹(20)

6. Graph the function f(x)=log3x. Label three points on the graph (one should be the intercept) with corresponding ordered pairs and label the asymptote with its equation. Write the domain and range of the function in interval notation. Make your graph big enough to see all important features.

Find the average value gave of the function g on the given interval. gave = g(x) = 8√√x, [8,64] Need Help? Read It Watch It

Chapter 14 Solutions

Loose-leaf Version For 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.

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), and points P=(2,2,8).

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