Question: Let S be the surface parametrized by R ( u , v )= u i + v j + a ( u + v )

Let S be the surface parametrized by R(u,v)=u i +v j +a(u+v) k , where 0u1, 0v1, and a is a parameter, and F the vector field defined by F(x,y,z)=x^2 i+xy j+(1z^2) k.

The surface S is oriented "upward."

(a) Find the Cartesian equation of S. What type of surface is it?

(b) For which value of the parameter a is the flux of F through S maximal?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Let $\mathcal{S}$ be the surface parametrized by \[ \Phi(u, v)=\left(2 u \sin \frac{v}{2}, 2 u \cos \frac{v}{2}, 3 vight) \] for $0 \leq u \leq 1$ and $0 \leq v \leq 2 \pi$ (a) Calculate the...

galindez (cmg3849) - Homework 13 (7.5,7.6,8.1,8.2) - tegtmeyer - (54045) This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page - find all choices...

Please answer these four question, no thorough explanation needed. Thank you. will leave good review. 4. [-/1 Points] DETAILS LARCALCET7 15.5.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find a...

3. (15 points) It is true that context-free languages are not closed under intersection. In this problem, we will show that if L is a context-free language and K is a regular language then LnK is...

Pick 5 large ( > $1 billion market cap) publicly traded companies that you might want to invest in. Make sure all 5 companies have been publicly traded with daily price data available in Yahoo...

Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point. r(u, v) = wi + vi + Wuvk, (1, 1, 1) 2 1 (1, 1, 1 ) Need Help? Read It /1 Points]...

You may nd it valuable for intuition to plot your solutions in CalcPlotBD when you nish each problem. 1. Consider the parametric surface S traced out by 1"(11, 1)) - (u: 1):, u + v,u 1.1/2). Compute...

r 'u V" V A r J "u . ' ' ' ' a . , 11 ' ' ,u _ _ ' 1:\" ' '1'; Ch 2.3 Product & Quotient! ' NISha Singh ' , 6 C' (Dwww.webassign.net/web/Student/Assignment-Responses/last?dep=15770928 i} G 5 Find the...

My project has 4 parts (i have already completed parts 1-3 which are excel sheets 1-3 as well) I only need help with completing part 4 (excel sheet 4) please feel free to work directly on my sheet!...

I need assistance with part 4 of this accounting exercise! Please when you attach your excel sheet or attach the work, ensure that the formulas/entries are in regards to my own excel sheet! thank...

Using the data in E4-2 and a piece of graph paper: 1. Plot the data points on the graph and draw a line by visual inspection, indicating the trend shown by the data points. 2. Determine the variable...

Suppose you are given the following bond quote information: Time to maturity: 10 years Current yield: 7.25% Coupon rate: 5.75% Par value: $1,000 Assuming semi-annual compounding, calculate the...

CIS 1 0 1 Final Exam nal Exam What is one of the advantages of data visualization? 5 2 Multiple Choice illustrates patterns in data hides complex data makes data less accessible reduces interactivity...

Please see image for question on the traveling salesman