This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 101 Exam December 1996 [10] 1. The region R is the portion of the first quadrant which is below the
parabola y2 = 8x and above the hyperbola y2 — x2 = 15. (a) Sketch the region R. (b) Find the volume of the solid obtained by revolving R about the 1:
axis. [10] 2. (a) Sketch the region bounded by y = In I, y = 0, z = 1, and x = 2. (b) Determine the volume of the solid obtained by revolving this region
about the y axis. [10] 63) Let L be the length of the part of the curve y = e" lying between
a: = 0 and z = 4. Use the Trapezoidal rule with four subintervals to estimate L. [12]. Let A denote the area of the plane region bounded by z' = 0, x = 1, y = 0, and y : le—Jr—z—f, where k is a positive constant. (8) Find the coordinates of the centroid of this region in terms of k
and A. (b) For what value of k is the centroid on the line y : x? A motor boat is traveling with a velocity of 40 ft/sec when its motor shuts off at time t = 0. Thereafter, its deceleration due to water
resistance is given by [12] where k is a positive constant. After 10 seconds, the boat’s velocity is
20 ft/sec. (a) What is the value of k? (b) When will the boat’s velocity be 5 ft/sec? [8] A 6 metre long cedar log has cross sections which are approximately
circular. The diameters of the log, measured at one metre intervals,
are given below: metres from left end of log 0 1 2 3 4 5 6
diameter in metres 1.2 1 0.8 0.8 l 1 Use Simpson’s rule to estimate the volume of the log. [12] 7. The portion of the ﬁrst quadrant which is below the curve y = i and
to the right of the line 1' = 1 is revolved about the x axis. (a) Determine the volume of the resulting solid. (b) Find the area of the surface of the solid. [14]@ Let 1(3) = f; 6";1 dt. (a) Find the Maclaurin series for (b) Approximate 1(1) to within $0.01. (c) Explain why your answer to part (b) has the desired accuracy. [12] 9. (a) Find the area of the plane region which is inside the cardiod
r = 1 + cos 9. (b) Sketch the region R which is inside the cardiod r = 1 + cos 0 and
outside the cardiod r = 1 + sin 9. (c) Determine the area of R. ...
View
Full Document
 Spring '08
 Broughton
 Math, Region, Euclidean geometry, plane region, metre long cedar

Click to edit the document details