University:
California State University, Northridge
Course:
MATH 250 | Calculus III
Academic year:

2015
Views:

490

Pages:

2
Author:

Offiplecraplep5c

Mon. Nov 9, 2015 MATH 250, Quiz 8 J'��&IH.J,· Name (print): Each problem is worth 2 points. Show all your work. ✓ 1. Let V be the volume of the solid that lies under the graph of f (x, y) = 52 - x 2 - y2 and above the rectangle R = (2, 4) x (2, 6). We use the lines x = 3 and y = 4 to divide R into subrectangles. Let L and U be the Riema�n sums computed using lower left corners and upper right corners, respectively. Without calculating the numbers V, L and U, arrange them in increasing order and explain your reasoning. � oif-e./-; T ef.ec v.e:a... .l.-e.S (;i(..,:t' t �c r.e � J.-4.$ 4, r:;v �d- ( J,1r-�e.:f �J?�·(. rk v�L.-s � -6-e. C'I.A,,) e...e.1-. r-t....e?. -� -e'ot.,.<..J€-v" c� va/dt...e. .,� �Q...X <,,4.,.f,c e:\. k- d � ""'"· �· -n...� Co-,,,i,,.ty- ---� ftt.e._1'e po,;,._ -1:J � ,,..,,.... 'L i, i 0 2. The integral JJR ✓9 - y2 w-?.e� L°> 2 J X [e, l/] dA represents the volume of a solid. Sketch the solid. 0) �, is) \ ( /2_ c �/�--1---��-.z---:;�> /� �r c� �o) c�zo) c12--+1t="l- =4 ""'J,e"' e:vc.l...e. 0j· l� � -f-C--. j� -r ..ec,....� ._-o+ deo'@...,,__J 1ivr ,s � <:;1,V\Jor c(ae .1 Please turn over...