MATH 220 Midterm: MATH220 CofC math220fa09

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turquoisegnu128

15 Feb 2019

School

College of Charleston

Department

Mathematics

Course

MATH 220

Professor

All

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Document Summary

Instructions: fully explain your answers and show your work. If you are not sure if you have written enough, please ask: (12 pts. ) 3 x3 for 0 x 1: (6 pts. ) Let r be the region between the graph y = x and the x-axis, for 0 x 4. Find the coordinates of the center of mass of this region: (5 pts. ) , y(0) = 5: (a) (5 pts. ) Find the approximate value of r . 8 intervals. 0 ln(1+x2) dx using simpson"s rule, with n = 4 (b) (5 pts. ) Find the approximate value of this integral, with error less than 1/100, using a power series: (16 pts. ) Find the following antiderivatives: (a) z x2 cosh x dx (b) z sec3 x tan x dx (c) z x 3 x3 + 9x dx (d) z. Evaluate the improper integral or show that it diverges: dx.

Related Questions

1. A water tank is in the shape of a paraboloid. Its shape is obtained by rotating the parabola y= .25x² , between x = 0 and x = 4, around the y-axis. x and y are in feet.

a. Find the volume of the tank.

b. The tank is full of water. Find the work required to pump the water out of the tank. (Water weighs 62.5 lbs per cubic foot.)

1) A water tank is in the shape of a paraboloic. Its shape is obtained by rotating the parabola y=.25x², between x=0 and x=4 around the y-axis. x and y are in feet

a) Find the volume for the tank

b) The tank is full of water. Find the work required to pump the water out of the tank ( Water weighs 62.5 lbs per cubic foot)

2) consider the function f(x)=x³-6x² +P, where P is a constant. Find the value of P so that the average value of f over the interval (-1,2) is 1.

3) a) sketch the graph of r=cos(2theta), for 0<theta<2pi

b) Find the area enclosed by one loop of the figure in your sketch

4) Consider the region in the first quadrant bounded by y=4x² , the y-axis, and the line y=4

a) Find the area of this region

b) Find the centroid of this region.

Use simpsons rule to approximate the fluid force of the 40 ftvertical wall.