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4 marksLimits

CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 2 · Question 5(a)(i)

Let f(x) be a function defined as f(x) = {ax + 2, x < 3; ax², x ≥ 3}.

Find the value of a if f(x) is continuous at x = 3.

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Other parts of this question

  1. 5(a)(ii)find the value of b.[5 marks]
  2. 5(b)(i)Let y = 1/√x. Using first principles, find dy/dx.[8 marks]
  3. 5(b)(ii)If y = x/√(1+x), determine an expression for dy/dx. Simplify the answer FULLY.[4 marks]
  4. 5(c)Find dy/dx in terms of θ. Simplify the answer as far as possible.[4 marks]

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