Unformatted text preview: Practice Exam 1 Math 1960 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x—axis. 1)y=x2+3.y=4x+3 1) t 5
Find the volume of the solid generated by revolving the region about the given line. I O 3‘33 2) The region bounded above by the line y = 16, below by the curve y = 16 — x2, and on the 2) 5
right by the line x z 4, about the line y = 16 Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x—axis. ﬁll“
3)x=2t\/y,x=-2y.y=1 3)__L6+_ Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method. (9mg?
4) The triangle with vertices (0. 0). (0, 2), and (4. 2) about the line x z 4 Find the length of the curve.
5) x=4sint+4t.y=4cost,05t:sit 6)y=2x3/2frornx=0tox:—:- 7)x=%-(y—1)3/2fromy=16toy=25 Find the area of the surface generated by revolving the curve about the indicated axis. - _ e I i
8) y = x3/14, 0 5 x :5 4; x—axis 8) 9) x=y3/9, Oeyez; y—axis 9) 5' Find the area of the surface generated by revolving the curves about the indicated axis. m Tie
10) x = sin t, y = 7 + cos t, O 5125 2n; Xmaxis 10) ’1
Solve the differential equation. .. L
2 ‘ “w”
11) 92’. = .521... 11) 5% t C
Solve the problem.
12) In a chemical reaction, the rate at which the amount of a reactant changes with time is 12) i
proportional to the amount present, such that ﬁg;- 2 -0.7y, when t is measured in hours. If there are 79 g of reactant present when t 2-: 0, how many grams will be left after 3 hours?
Give your answer to the nearest tenth of a grain. 13) The spring of a spring balance is 7.0 in. long when there is no weight on the balance, and it is 9.2 in. long with 4.0 lb hung from the balance. How much work is done in stretching it
from 7.0 in. to a length of 12.1 in? 14) A vertical right circular cylindrical tank measures 24 ft high and 16 ft in diameter. It is full of oil weighing 60 lb/ft3. How much work does it take to pump the oil to a leve12 ft above
the t0p of the tank? Give your answer to the nearest ft - lb. pump the gasoline to a level 16 ft above the cone's top? Give your answer to the nearest ft - 1b. Find the center of mass of a thin plate of constant density covering the given region.
16) The region bounded by y = x2 and y = 9 ...
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