Question 1 (17 marks) Letf : S C R+ —> Rbe given by_ J? — 1flX) _ X _ 1(a) Use Theorem 2.2 to deriveLim f(x).x41(2 marks)(b) Is f continuous at the pointx = 1?Briefly explain.(2 marks)(c) According to Definition 2.1 what do you need to show to prove that f is continuous atJC() 6 S.( 2 marks)(d) Show thatl 1— — < — .(4 marks)(e) Use the result in (d) to prove that f is continuous at x0 6 S. Hint: SinceJJC—o Z 0,it follows thatJ— – JJTo S J17 + M .(7 marks)


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