Question 1 (ii) 1. Produce an example of a function with the described characteristics. You may use any valid way ofdefining a function (such as using piecewise functions). Give the limit calculations to show that yourfunction satisfies these conditions. You should aim to produce the simplest possible example to makeyour 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, definef (c+h)-f(c- h)|f(c) = limh 02hCompute 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) 1f.P and alæ) =f (x)2. If the table below describes the val

Name: Question 1 (ii) 1. Produce an example of a function with the described
Uploaded: 2024-03-20T07:07:50.000Z
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Description: Question 1 (ii) 1. Produce an example of a function with the described characteristics. You may use any valid way ofdefining a function (such as using piecewise functions). Give the limit calculations to show that yourfunction satisfies these conditi