1. Produce an example of a function with the described characteristics. You may use any valid way of defining a function (such as using piecewise functions). Give the limit calculations to show that...

Question 1 (ii)

Extracted text: 1. Produce an example of a function with the described characteristics. You may use any valid way of defining a function (such as using piecewise functions). Give the limit calculations to show that your function satisfies these conditions. You should aim to produce the simplest possible example to make your work readable. (i) A function with exactly one jump discontinuity at the point r = 2. (ii) ( A function with exactly two removable discontinuities. (iii) A function with exactly one jump discontinuity and exactly one essential discontinuity. 2. If f is a function and c is some point in the domain of f, define f (c+h)-f(c- h) | f(c) = lim h 0 2h Compute f(2) when f(x) = 1/r. Show that f(2) = f'(2). (You do not need to fir (i) - - f'(x) by first principles.) /- Show that f(æ) = f' (x) for all a ER when f(x) = x². (You do not need to find f' %3D (ii) by first principles.) | Compute the value of f(0) when f(x) = |r|. Explain why f cannot be the derivativ %3D (iii) 1 f. P and alæ) = f (x)2. If the table below describes the val