{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Wksht2 - Math 17C Kouba Worksheet 2 1 Let R be the region...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 17C Kouba Worksheet 2 1.) Let R be the region bounded by the graphs of y : x3. and y = 4:10 (in the first quadrant). Describe R using vertical cross—sections. b.) Describe R using horizontal cross—sections. 2.) Let R be the region inside the circle of radius 2 centered at (0,0) and above the y-axis. a.) Describe R using vertical cross-sections. b.) Describe R using horizontal cross-sections. 3.) Let R be the triangular region with vertices (0,0), (—2, 3), and (2, 3). a.) Describe R using vertical cross-sections. b.) Describe R using horizontal cross-sections. 4.) Let R be the region bounded by the graphs of x = y2 and :1: = 2 — y2 . a.) Describe R using vertical cross-sections. b.) Describe R using horizontal cross-sections. 5.) Sketch each of the following regions described in two—dimensional space. a.)0§$§1,3xSyS$-+~2 b.)0$xgln4,emgyg4 C~)1SyS4,—\/§SxS\/17 d~)1Sysln5,1nySmSey 6.) Evaluate the following double integrals. 3 1 1 2 $69; a.) / / (1 +4xy)drcdy b.) / / —dyd:r 1 0 0 1 y 2 1 8 1 -1 my c.) / / 2m+y) dxdy d.) / / ————————-dydx 0 0 ( 0 0 «3:2 + y2 + 1 1 m2 1 6" e.) / / (a: + 2y) dy dz f.) / / Vida: dy 0 0 0 y 7r/2 cos y . 1r/4 7r/6 g.) / / 65‘“ 3’ dz): dy h.) / / cos 3m sin 2y dy dm 0 0 0 0 (Beware of the next two.) 1 3 1 1 i.) / / e$2 day dy j.) / / V 2:3 +1drcdy 0 3y 0 fl 1 7.) Find the area of the region a.) in problem 1. b.) in problem 4. 8.) Consider a mountain range above the grid 0 S x S 5, 0 S y S 8, where distance is measured in miles. Elevation (miles) above sea level at the point (13,34) is given by H(a:, y) = (1/40)(10 — m2 + yz). a.) Find the elevation at the points (0,0), (4, 2), and (0,8). b.) Compute the average elevation of this mountain range. 9.) A flat plate lies in region R bounded by the graphs of y = fl and y = (1/2):c. Temperature at point (x, y) is given by T(m, y) = 50 + 2x + y (0F). a.) Find the area of the plate. b.) Find the average width of the plate. c.) Find the average height of the plate. d.) Find the temperature at the points (0,0), (2, 1.1), and (4, 2). e.) Find the average temperature of the plate. 10.) Sketch the solid in 3D-Space whose volume is given by the following double integral. 1 yl/S / / (4—:c2—y2)d:rdy 0 0 11.) A flat plate lies in region R bounded by the graphs of :1: 2: 0, y = $3, and y = 1'2 + 4. Density at point (x, y) is given by 6(1), y) = 1 + .7: + 2y grams per square centimeter. a.) Find the area of the plate. b.) Find the average width of the plate. c.) Find the average height of the plate. d.) Find the density at the points (0,0), (1,3), and (2,8). e.) Find the average density of the plate. f.) Find the total mass of the plate. 12.) Compute the volume of the solid lying above the region bounded by the graphs of y = 2:5, y = 2, and :1: = O and below the paraboloid z = .132 + y2. 13.) Compute the volume of the solid which is above the region bounded by the graphs of y=cr2, y=0, andzr:2 and between the planeS$+y+z=6and$—y+z= 12. ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern