MATH 104 Midterm: MATH 104 UPenn Exam m104 sExam 1
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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 ââ°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.
x = 2y
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 âËâ 4x2 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 âËâ (y âËâ 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 |
