Try the fastest way to create flashcards
Question

# Determine which value best approximates the volume of the solid between the $x y$ plane and the function over the region. (Make your selection on the basis of a sketch of the solid and not by performing any calculations.) $f(x, y)=4 x$ $R$ : square with vertices $(0,0),(4,0),(4,4),(0,4)$ (a) $-200$ (b) $600$ (c ) $50$ (d) $125$ (e) $1000$

Solution

Verified
Step 1
1 of 2

The volume of the region can be approximated as height of the region times the area of the base. Since the area in $xy$ plane is a square with the area equal to $16$ and the function $f(x,y)=4x$ is positive over the given region any negative answer can be eliminated. Next, 50 is a bit too small while 600 or 1000 is a bit too much since $4x$ does not grow that rapidly or that slowly. The most educated guess is then d), 125.

## Recommended textbook solutions #### Thomas' Calculus

14th EditionISBN: 9780134438986 (11 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir
10,142 solutions #### Calculus

9th EditionISBN: 9780547167022 (13 more)Bruce H. Edwards, Ron Larson
13,318 solutions #### Calculus: Early Transcendentals

8th EditionISBN: 9781285741550 (5 more)James Stewart
11,084 solutions #### Calculus: Early Transcendentals

9th EditionISBN: 9781337613927Daniel K. Clegg, James Stewart, Saleem Watson
11,050 solutions