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# Let In y y2 0 sinn x dx. (a) Show that I2n12 < I2n11 < I2n. (b) Use Exercise 50 to show

ISBN: 9781305270336 484

## Solution for problem 74 Chapter 7.1

Single Variable Calculus: Early Transcendentals | 8th Edition

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Problem 74

Let In y y2 0 sinn x dx. (a) Show that I2n12 < I2n11 < I2n. (b) Use Exercise 50 to show that I2n12 I2n 2n 1 1 2n 1 2 (c) Use parts (a) and (b) to show that 2n 1 1 2n 1 2 < I2n11 I2n < 1 and deduce that limnl I2n11yI2n 1. (d) Use part (c) and Exercises 49 and 50 to show that lim nl 2 1 ? 2 3 ? 4 3 ? 4 5 ? 6 5 ? 6 7 ? ? 2n 2n 2 1 ? 2n 2n 1 1 2 This formula is usually written as an infinite product: 2 2 1 ? 2 3 ? 4 3 ? 4 5 ? 6 5 ? 6 7 ? and is called the Wallis product. (e) We construct rectangles as follows. Start with a square of area 1 and attach rectangles of area 1 alternately beside or on top of the previous rectangle (see the figure). Find the limit of the ratios of width to height of these rectangles.

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TERMS OF CONTRACT General Issue Description Statute/Case Description Rule/Excepti on Issue 1: Is the statement a puff, representation or a term Puf Pufs are imprecise statements that tend to be exaggerated. This can be supported by the Koh Wee Meng v Trans Eurokars (2014) case where the court held that the description of the car “whisper-quiet interior” and “magic carpet ride” was a mere puf. If not puff: In this case, the statement is not a puf because details such as _______ are given. Representatio Representations are statements n which have induced t

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