Solve the problem.The half-life of an element is 4.4 × 1012 yr. How long does it take a sample of the element to decay to 
of its original mass? Use 
where A0 is the initial amount, T is the half-life, and t is the time. (Express results in scientific notation, rounded to the nearest hundredth.)
A. 2.79 × 1012 yr
B. 5.82 × 1012 yr
C. 9.82 × 1011 yr
D. 4.32 × 1012 yr
Answer: B
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Use integration by parts to establish a reduction formula for the integral.
A. 
= - 
+ 
B. 
= - 
+ 
C. 
= - axn e-ax + na 
D. 
= 
- 
Find all the first order partial derivatives for the following function.f(x, y) = 
A. fx(x, y) = - 
; fy(x, y) = - 
B. fx(x, y) = - 
; fy(x, y) = - 
C. fx(x, y) = - 
; fy(x, y) = - 
D. fx(x, y) = 
; fy(x, y) = 
Evaluate the integral.
A. 18x sin 
x - 36 cos 
x + C
B. 72 sin 
x - 36x cos 
x + C
C. 18 sin 
x + 36x cos 
x + C
D. 36x sin 
x + 72 cos 
x + C
Solve the problem.The local clothing store marks up the price that it pays to the clothing manufacturer by 32%. If the selling price of a pair of jeans is $124, how much did the clothing store pay for the jeans?
A. $163.68 B. $182.35 C. $29.52 D. $93.94