3. (i) Consider the function f: RR defined by f(:2) = x -2,1 <0. 2. = 0, 2.c?, >0. Use the sequence (Heine) form of the

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3 I Consider The Function F Rr Defined By F 2 X 2 1 0 2 0 2 C 0 Use The Sequence Heine Form Of The 1 (24.93 KiB) Viewed 24 times

3. (i) Consider the function f: RR defined by f(:2) = x -2,1 <0. 2. = 0, 2.c?, >0. Use the sequence (Heine) form of the definition of limit to prove that I is not continuous at xo = 0. 18 Marks) (ii) Use the Intermediate Value Theorem to prove that there exists c € (-2,5) such that 4 sin(c) = 62. |Hint: consider the function 9:1-9,51 → R defined by g(x) = 4 sin(x) – 22. You may assume without proof that g is continuous on (-5,5)/ 15 Marks