Find a function P(x) of least possible degree, having real coefficients, with the given zeros.5 and 4i
A. P(x) = x3 + 5x2 + 16x - 80
B. P(x) = x3 - 5x2 + 16x - 80
C. P(x) = x3 - 5x2 - 16x - 80
D. P(x) = x3 - 5x2 + 16x + 80
Answer: B
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Find all the second order partial derivatives of the given function.f(x, y) = ln (x2y - x)
A. 
= 
; 
= - 
; 
= 
= - 
B. 
= 
; 
= - 
; 
= 
= - 
C. 
= 
; 
= 
; 
= 
= 
D. 
= 
; 
= - 
; 
= 
= - 
The figure below is a square ABCD with center O. (M, N, P, and Q are the midpoints of the sides.)
The image of A under a 90° clockwise rotation with center O is
A. M. B. B. C. D. D. C. E. none of these
Figure (a) shows a vacant lot with a 100-ft frontage in a development. To estimate its area, we introduce a coordinate system so that the x-axis coincides with the edge of the straight road forming the lower boundary of the property, as shown in Figure (b). Then, thinking of the upper boundary of the property as the graph of a continuous function f over the interval [0, 100], we see that the problem is mathematically equivalent to that of finding the area under the graph of f on [0, 100]. To estimate the area of the lot using a Riemann sum, we divide the interval [0, 100] into five equal subintervals of length 20 ft. Then, using surveyor's equipment, we measure the distance from the midpoint of each of these subintervals to the upper boundary of the property. These measurements give the
values of f(x) at x = 10, 30, 50, 70, and 90. What is the approximate area of the lot?
?
?
?
__________ square feet
Fill in the blank(s) with the appropriate word(s).
Find the general solution of the differential equation.
= 21x2
A. 21x3 + C
B. 
+ C
C. x3 + C
D. 7x3 + C