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.

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