APPLIED CALCULUS (WILEY PLUS)
6th Edition
ISBN: 9781119399322
Author: Hughes-Hallett
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Question
Chapter 8.3, Problem 30P
To determine
To calculate:
The value of the function
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
show full work please
3. Describe the steps you would take to find the absolute max of the following
function using Calculus f(x) = :
, [-1,2]. Then use a graphing calculator to
x-1
x²-x+1
approximate the absolute max in the closed interval.
(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz).
Ꮖ
(a) (4 points) Show that V x F = 0.
(b) (4 points) Find a potential f for the vector field F.
(c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use
Stokes' Theorem to calculate the line integral
Jos
F.ds;
as denotes the boundary of S. Explain your answer.
Chapter 8 Solutions
APPLIED CALCULUS (WILEY PLUS)
Ch. 8.1 - Prob. 1PCh. 8.1 - Prob. 2PCh. 8.1 - Prob. 3PCh. 8.1 - Prob. 4PCh. 8.1 - Prob. 5PCh. 8.1 - Prob. 6PCh. 8.1 - Prob. 7PCh. 8.1 - Prob. 8PCh. 8.1 - Prob. 9PCh. 8.1 - Prob. 10P
Ch. 8.1 - Prob. 11PCh. 8.1 - Prob. 12PCh. 8.1 - Prob. 13PCh. 8.1 - Prob. 14PCh. 8.1 - Prob. 15PCh. 8.1 - Prob. 16PCh. 8.1 - Prob. 17PCh. 8.1 - Prob. 18PCh. 8.1 - Prob. 19PCh. 8.1 - Prob. 20PCh. 8.1 - Prob. 21PCh. 8.1 - Prob. 22PCh. 8.1 - Prob. 23PCh. 8.1 - Prob. 24PCh. 8.1 - Prob. 25PCh. 8.1 - Prob. 26PCh. 8.1 - Prob. 27PCh. 8.1 - Prob. 28PCh. 8.1 - Prob. 29PCh. 8.1 - Prob. 30PCh. 8.2 - Prob. 1PCh. 8.2 - Prob. 2PCh. 8.2 - Prob. 3PCh. 8.2 - Prob. 4PCh. 8.2 - Prob. 5PCh. 8.2 - Prob. 6PCh. 8.2 - Prob. 7PCh. 8.2 - Prob. 8PCh. 8.2 - Prob. 9PCh. 8.2 - Prob. 10PCh. 8.2 - Prob. 11PCh. 8.2 - Prob. 12PCh. 8.2 - Prob. 13PCh. 8.2 - Prob. 14PCh. 8.2 - Prob. 15PCh. 8.2 - Prob. 16PCh. 8.2 - Prob. 17PCh. 8.2 - Prob. 18PCh. 8.2 - Prob. 19PCh. 8.2 - Prob. 20PCh. 8.2 - Prob. 21PCh. 8.2 - Prob. 22PCh. 8.2 - Prob. 23PCh. 8.2 - Prob. 24PCh. 8.2 - Prob. 25PCh. 8.2 - Prob. 26PCh. 8.2 - Prob. 27PCh. 8.2 - Prob. 28PCh. 8.2 - Prob. 29PCh. 8.2 - Prob. 30PCh. 8.2 - Prob. 31PCh. 8.2 - Prob. 32PCh. 8.2 - Prob. 33PCh. 8.2 - Prob. 34PCh. 8.2 - Prob. 35PCh. 8.2 - Prob. 36PCh. 8.2 - Prob. 37PCh. 8.2 - Prob. 38PCh. 8.2 - Prob. 39PCh. 8.2 - Prob. 40PCh. 8.2 - Prob. 41PCh. 8.2 - Prob. 42PCh. 8.2 - Prob. 43PCh. 8.2 - Prob. 44PCh. 8.3 - Prob. 1PCh. 8.3 - Prob. 2PCh. 8.3 - Prob. 3PCh. 8.3 - Prob. 4PCh. 8.3 - Prob. 5PCh. 8.3 - Prob. 6PCh. 8.3 - Prob. 7PCh. 8.3 - Prob. 8PCh. 8.3 - Prob. 9PCh. 8.3 - Prob. 10PCh. 8.3 - Prob. 11PCh. 8.3 - Prob. 12PCh. 8.3 - Prob. 13PCh. 8.3 - Prob. 14PCh. 8.3 - Prob. 15PCh. 8.3 - Prob. 16PCh. 8.3 - Prob. 17PCh. 8.3 - Prob. 18PCh. 8.3 - Prob. 19PCh. 8.3 - Prob. 20PCh. 8.3 - Prob. 21PCh. 8.3 - Prob. 22PCh. 8.3 - Prob. 23PCh. 8.3 - Prob. 24PCh. 8.3 - Prob. 25PCh. 8.3 - Prob. 26PCh. 8.3 - Prob. 27PCh. 8.3 - Prob. 28PCh. 8.3 - Prob. 29PCh. 8.3 - Prob. 30PCh. 8.3 - Prob. 31PCh. 8.3 - Prob. 32PCh. 8.3 - Prob. 33PCh. 8.3 - Prob. 34PCh. 8.3 - Prob. 35PCh. 8.3 - Prob. 36PCh. 8.3 - Prob. 37PCh. 8.3 - Prob. 38PCh. 8.3 - Prob. 39PCh. 8.3 - Prob. 40PCh. 8.4 - Prob. 1PCh. 8.4 - Prob. 2PCh. 8.4 - Prob. 3PCh. 8.4 - Prob. 4PCh. 8.4 - Prob. 5PCh. 8.4 - Prob. 6PCh. 8.4 - Prob. 7PCh. 8.4 - Prob. 8PCh. 8.4 - Prob. 9PCh. 8.4 - Prob. 10PCh. 8.4 - Prob. 11PCh. 8.4 - Prob. 12PCh. 8.4 - Prob. 13PCh. 8.4 - Prob. 14PCh. 8.4 - Prob. 15PCh. 8.4 - Prob. 16PCh. 8.4 - Prob. 17PCh. 8.4 - Prob. 18PCh. 8.4 - Prob. 19PCh. 8.4 - Prob. 20PCh. 8.4 - Prob. 21PCh. 8.4 - Prob. 22PCh. 8.4 - Prob. 23PCh. 8.4 - Prob. 24PCh. 8.4 - Prob. 25PCh. 8.4 - Prob. 26PCh. 8.4 - Prob. 27PCh. 8.4 - Prob. 28PCh. 8.4 - Prob. 29PCh. 8.4 - Prob. 30PCh. 8.4 - Prob. 31PCh. 8.4 - Prob. 32PCh. 8.4 - Prob. 33PCh. 8.4 - Prob. 34PCh. 8.4 - Prob. 35PCh. 8.4 - Prob. 36PCh. 8.4 - Prob. 37PCh. 8.4 - Prob. 38PCh. 8.4 - Prob. 39PCh. 8.4 - Prob. 40PCh. 8.4 - Prob. 41PCh. 8.4 - Prob. 42PCh. 8.4 - Prob. 43PCh. 8.4 - Prob. 44PCh. 8.5 - Prob. 1PCh. 8.5 - Prob. 2PCh. 8.5 - Prob. 3PCh. 8.5 - Prob. 4PCh. 8.5 - Prob. 5PCh. 8.5 - Prob. 6PCh. 8.5 - Prob. 7PCh. 8.5 - Prob. 8PCh. 8.5 - Prob. 9PCh. 8.5 - Prob. 10PCh. 8.5 - Prob. 11PCh. 8.5 - Prob. 12PCh. 8.5 - Prob. 13PCh. 8.5 - Prob. 14PCh. 8.5 - Prob. 15PCh. 8.5 - Prob. 16PCh. 8.5 - Prob. 17PCh. 8.5 - Prob. 18PCh. 8.5 - Prob. 19PCh. 8.5 - Prob. 20PCh. 8.5 - Prob. 21PCh. 8.5 - Prob. 22PCh. 8.5 - Prob. 23PCh. 8.5 - Prob. 24PCh. 8.5 - Prob. 25PCh. 8.5 - Prob. 26PCh. 8.5 - Prob. 27PCh. 8.5 - Prob. 28PCh. 8.5 - Prob. 29PCh. 8.5 - Prob. 30PCh. 8.5 - Prob. 31PCh. 8.5 - Prob. 32PCh. 8.6 - Prob. 1PCh. 8.6 - Prob. 2PCh. 8.6 - Prob. 3PCh. 8.6 - Prob. 4PCh. 8.6 - Prob. 5PCh. 8.6 - Prob. 6PCh. 8.6 - Prob. 7PCh. 8.6 - Prob. 8PCh. 8.6 - Prob. 9PCh. 8.6 - Prob. 10PCh. 8.6 - Prob. 11PCh. 8.6 - Prob. 12PCh. 8.6 - Prob. 13PCh. 8.6 - Prob. 14PCh. 8.6 - Prob. 15PCh. 8.6 - Prob. 16PCh. 8.6 - Prob. 17PCh. 8.6 - Prob. 18PCh. 8.6 - Prob. 19PCh. 8.6 - Prob. 20PCh. 8.6 - Prob. 21PCh. 8.6 - Prob. 22PCh. 8.6 - Prob. 23PCh. 8.6 - Prob. 24PCh. 8.6 - Prob. 25PCh. 8.6 - Prob. 26PCh. 8.6 - Prob. 27PCh. 8 - Prob. 1SYUCh. 8 - Prob. 2SYUCh. 8 - Prob. 3SYUCh. 8 - Prob. 4SYUCh. 8 - Prob. 5SYUCh. 8 - Prob. 6SYUCh. 8 - Prob. 7SYUCh. 8 - Prob. 8SYUCh. 8 - Prob. 9SYUCh. 8 - Prob. 10SYUCh. 8 - Prob. 11SYUCh. 8 - Prob. 12SYUCh. 8 - Prob. 13SYUCh. 8 - Prob. 14SYUCh. 8 - Prob. 15SYUCh. 8 - Prob. 16SYUCh. 8 - Prob. 17SYUCh. 8 - Prob. 18SYUCh. 8 - Prob. 19SYUCh. 8 - Prob. 20SYUCh. 8 - Prob. 21SYUCh. 8 - Prob. 22SYUCh. 8 - Prob. 23SYUCh. 8 - Prob. 24SYUCh. 8 - Prob. 25SYUCh. 8 - Prob. 26SYUCh. 8 - Prob. 27SYUCh. 8 - Prob. 28SYUCh. 8 - Prob. 29SYUCh. 8 - Prob. 30SYUCh. 8 - Prob. 31SYUCh. 8 - Prob. 32SYUCh. 8 - Prob. 33SYUCh. 8 - Prob. 34SYUCh. 8 - Prob. 35SYUCh. 8 - Prob. 36SYUCh. 8 - Prob. 37SYUCh. 8 - Prob. 38SYUCh. 8 - Prob. 39SYUCh. 8 - Prob. 40SYUCh. 8 - Prob. 41SYUCh. 8 - Prob. 42SYUCh. 8 - Prob. 43SYUCh. 8 - Prob. 44SYUCh. 8 - Prob. 45SYUCh. 8 - Prob. 46SYUCh. 8 - Prob. 47SYUCh. 8 - Prob. 48SYUCh. 8 - Prob. 49SYUCh. 8 - Prob. 50SYUCh. 8 - Prob. 51SYUCh. 8 - Prob. 52SYUCh. 8 - Prob. 53SYUCh. 8 - Prob. 54SYUCh. 8 - Prob. 55SYUCh. 8 - Prob. 56SYUCh. 8 - Prob. 57SYUCh. 8 - Prob. 58SYUCh. 8 - Prob. 59SYUCh. 8 - Prob. 60SYUCh. 8 - Prob. 1FOTCh. 8 - Prob. 2FOTCh. 8 - Prob. 3FOTCh. 8 - Prob. 4FOTCh. 8 - Prob. 5FOTCh. 8 - Prob. 6FOTCh. 8 - Prob. 7FOT
Knowledge Booster
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
- (3) (16 points) Consider z = uv, u = x+y, v=x-y. (a) (4 points) Express z in the form z = fog where g: R² R² and f: R² → R. (b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by T(x, y) = (x, y, ƒ (g(x, y)) (x, y) = R². Give a parametric description of the tangent plane to S at the point p = T(x, y). (d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic approximation) of F = (fog) at a point (a, b). Verify that Q(x,y) F(a+x,b+y). =arrow_forward(6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0arrow_forward(10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward
- (1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward(9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward(8) (12 points) (a) (8 points) Let C be the circle x² + y² = 4. Let F(x, y) = (2y + e²)i + (x + sin(y²))j. Evaluate the line integral JF. F.ds. Hint: First calculate V x F. (b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux integral √(V × F) F).dS. Justify your answer.arrow_forward
- Determine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. a = 13, b = 15, C = 68° Law of Sines Law of Cosines Then solve the triangle. (Round your answers to four decimal places.) C = 15.7449 A = 49.9288 B = 62.0712 × Need Help? Read It Watch Itarrow_forward(4) (10 points) Evaluate √(x² + y² + z²)¹⁄² exp[}(x² + y² + z²)²] dV where D is the region defined by 1< x² + y²+ z² ≤4 and √√3(x² + y²) ≤ z. Note: exp(x² + y²+ 2²)²] means el (x²+ y²+=²)²]¸arrow_forward(2) (12 points) Let f(x,y) = x²e¯. (a) (4 points) Calculate Vf. (b) (4 points) Given x directional derivative 0, find the line of vectors u = D₁f(x, y) = 0. (u1, 2) such that the - (c) (4 points) Let u= (1+3√3). Show that Duƒ(1, 0) = ¦|▼ƒ(1,0)| . What is the angle between Vf(1,0) and the vector u? Explain.arrow_forward
- Find the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a b 29 39 66.50 C 17.40 d 0 54.0 126° a Ꮎ b darrow_forward(5) (10 points) Let D be the parallelogram in the xy-plane with vertices (0, 0), (1, 1), (1, 1), (0, -2). Let f(x,y) = xy/2. Use the linear change of variables T(u, v)=(u,u2v) = (x, y) 1 to calculate the integral f(x,y) dA= 0 ↓ The domain of T is a rectangle R. What is R? |ǝ(x, y) du dv. |ð(u, v)|arrow_forward2 Anot ined sove in peaper PV+96252 Q3// Find the volume of the region between the cylinder z = y2 and the xy- plane that is bounded by the planes x=1, x=2,y=-2,andy=2. vertical rect a Q4// Draw and Evaluate Soxy-2sin (ny2)dydx D Lake tarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage


Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning

Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell

Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill

Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Chain Rule dy:dx = dy:du*du:dx; Author: Robert Cappetta;https://www.youtube.com/watch?v=IUYniALwbHs;License: Standard YouTube License, CC-BY
CHAIN RULE Part 1; Author: Btech Maths Hub;https://www.youtube.com/watch?v=TIAw6AJ_5Po;License: Standard YouTube License, CC-BY