MATH 1172 Study Guide - Final Guide: Cartesian Coordinate System

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violetmallard812

4 Dec 2017

School

Ohio State University

Department

Mathematics

Course

MATH 1172

Professor

James Talamo

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$MATH 1172 Full Course Notes$

MATH 1172 Full Course Notes

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Document Summary

12 y and x=10 with semicircular cross sections to the x axis: set up the integral to find the volume of the solid bounded by the functions. 25 and y=0: rotated about the line x=10, rotated about y=4, find the total area enclosed between the curves x when y. 3 sin ( ) cos ( ) x dx x. 1 n: find the interval of convergence of the follow power series. (do not worry about the end points of the interval!) ( 5) n. 3) n: approximate sin using the first four non zero terms of the taylor series about. 0 a) b) a x f x x. 6 c: consider the parametric curve x cos , t y. 0 a d dx x a) determine in terms of t and evaluate it at t . 1 t: consider the parametric curve x ln , t y t t.

Related Questions

I need help solving some problems including area bounded by aregion and volume by cylindrical shells.

1) y = 3/x

y=12x

y=1/12x

x>0

2)
Find thevolume V of the solid obtained by rotating the regionbounded by the given curves about the specifiedline.

y=4-(1/2x)

y=0

x=2

x=3

rotated about xaxis

3)Find thevolume V of the solid obtained by rotating the regionbounded by the given curves about the specified line.
x = 4sqrt(5y)

x=0

y=3

rotated on y axis

4)Find the volume V of the solid obtained by rotatingthe region bounded by the given curves about the specifiedline.
y = ln3x

y =4

y =5

x = 0

rotated on yaxis

5)
Find the volume V of the solid obtained by rotating theregion bounded by the given curves about the specified line.

y =3x⁵

y =3x

x Ã¢â°Â¥ 0

rotated on X axis

6)
Find the volume V of the solid obtained by rotating theregion bounded by the given curves about the specifiedline.

y² = 2x
x = 2y

about the y-axis

7)A CAT scan produces equally spaced cross-sectional views of ahuman organ that provide information about the organ otherwiseobtained only by surgery. Suppose that a CAT scan of a human livershows cross-sections spaced 1.5 cm apart. The liver is 15 cm longand the cross-sectional areas, in square centimeters, are 0,17, 58, 79,95, 107, 118, 129, 64, 39,and 0. Use the Midpoint Rule with n = 5 to estimate thevolume V of the liver.

8)
Let S be the solid obtained by rotating the region shown inthe figure about the y-axis. (Assume a = 7 and b = 2.)
y=ax(x-b)^2
What are its circumference c and height h?
Use shells to find the volume V of S.

9) Let S be the solid obtained by rotating the region shownin the figure about the y-axis. (Assume a = 4 andb = 2.)
y=asin(bx^2)

What are its circumference c andheight h?
Use shells to find the volume V of S.

10)Use the method of cylindrical shells to find the volumegenerated by rotating the region bounded by the given curves aboutthe y-axis.

y = 2x²
y = 12x Ã¢Ëâ 4x^2

11)Use the method of cylindrical shells to find thevolume of the solid obtained by rotating the region bounded by thegiven curves about the x-axis.

xy = 3
x =0
y =3
y =5

12)
Use the method of cylindrical shells to find the volume V ofthe solid obtained by rotating the region bounded by the givencurves about the x-axis.

x + y = 5
x = 9 Ã¢Ëâ (y Ã¢Ëâ 2)²

13)Use the method of cylindrical shells to find the volume Vgenerated by rotating the region bounded by the given curves aboutthe y-axis.

y = 5x²
y = 0
x = 1

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.

MATH 1172 Study Guide - Final Guide: Cartesian Coordinate System

MATH 1172 Full Course Notes

Document Summary

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