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Firefox File Edit View History Bookmarks Tools Window Help GODO 100% [7. Thu 19:04 Q OF . . . G prove PAn+ 137 1920_P 14.8 A proo $53 real analysis Job Desmos | G S How do you ( MAT137 We 137 192( X y! coursehero *Homework + @ A https://www.math.toronto.edu/zaman/137/PS/137_1920_PS10.pdf ... Q Search t 2 of 2 Automatic Zoom + 2. Approximations only hold value if you can estimate the error of your approximation. Often only a certain error threshold is tolerable. This leads to a natural question: What order of approximation N do I need to estimate - my function at x with d digits of accuracy? The answer depends on the function f, the value x at which you want to approximate it, and the distance between r and the centre of your approximation. It is helpful to express / in terms of a simple inequality involving d and x. Let N E N+. Let Py(x) be the Nth Taylor polynomial of et centred at 0. (a) Define RN(x) = ex - Pv(x) to be the Nth remainder term. Show that Vr > 0, [RN(x) > 0 with arbitrary accuracy. To more simply estimate the quality of your error term, it helps to understand precisely how factorials grow. Stirling's approximation says that Vn ENt, V 2 an" the "