(1) The parts in this question are not related to each other. 4 (a) Using thee – ôdefinition of limit, prove that limz3 3r – 1 (b) Letf: R→ R be a function with the following property: Ma) - Ab)| s...

Extracted text: (1) The parts in this question are not related to each other. 4 (a) Using thee – ôdefinition of limit, prove that limz3 3r – 1 (b) Letf: R→ R be a function with the following property: Ma) - Ab)| s 4|a - b| for all a,b E R. Prove that fis continuous everywhere. (c) Show that the function g(x) = x3 - 7x2 + 25x + 8 has exactly one real root. 112