WORKSHEET 36 - Fall 1995 1. Compute Z π/ 2-π/ 2 sin(3 x )cos(5 x ) dx. 2. It is known that m parts (by weight) of chemical A combine with n parts of chemical B to produce a comound C. Suppose that the rate at which C is produced varies directly with the product of the amounts of A and B present at that instant. Find the amount of C produced in t minutes from an intitial mixing of A0 pounds of A with B0 pounds of B, given that a) n = m , A0 = B0 .and A0 pounds of C are produced in the ±rst minute. b) n = m , A0 = 1 2 B0 .and A0 pounds of C are produced in the ±rst minute. c) n 6 = m , A0 = B0 .and A0 pounds of C are produced in the ±rst minute. 3. Find the fallacy in the following argument that 0 = 1. u = 1 x du = − 1 x 2 dx dv = dx v = x So integration by parts applied to R 1 /x dx yields: 0+ Z dx x = ± 1 x ² x − Z ± − 1 x 2 ² xdx =1+ Z dx x. Thus 0 = 1. 4. Compute
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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.