Unformatted text preview: y (0) = 2. Include any extreme values (maxima and minima), asymptotes, concavity, and inﬂection points. (12) Find the maximum value of the function f ( x,y ) = 2 x + 4 y subject to the constraint x 2 + y 2 = 1. (13) Is the function f ( x ) = if x < sin( x ) if 0 ≤ x ≤ 5 π/ 2 if x > 5 π/ 2 a probability density function? Justify your answer. (14) Use Simpson’s rule with n = 2 subdivisions to approximate Z 3 1 1 x dx. Express your answer as a fraction p/q with p and q whole numbers. (15) In a certain class, 25% of students attend lecture on any given day. If all of the students complete an online survey about their attendance for the most recent lecture, what is the probability that the ﬁrst student to complete the survey who attended lecture was the second student to complete the survey overall? 1...
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- Fall '08
- Probability theory, probability density function, Cumulative distribution function