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4 marksLimits

CAPE Pure Mathematics Unit 1 · May/June 2016 · Paper 2 · Question 6(b)(i)

A function f is defined on ℝ as f(x) = x² + 2x + 3 for x ≤ 0 and f(x) = ax + b for x > 0.

Calculate the lim (x→0⁻) f(x) and lim (x→0⁺) f(x).

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Other parts of this question

  1. 6(a)Find the equation of the tangent to the curve f(x) = 2x³ + 5x² – x + 12 at the point where x = 3.[4 marks]
  2. 6(b)(ii)Hence, determine the values of a and b such that f(x) is continuous at x = 0.[5 marks]
  3. 6(b)(iii)If the value of b = 3, determine a such that f'(0) = lim (t→0) (f(0 + t) - f(0)) / t.[6 marks]
  4. 6(c)Use first principles to differentiate f(x) = √x with respect to x.[6 marks]

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