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HCI Tutorial 3A Question 2

HCI Tutorial 3A Question 2

Find the set of values of \(x\) which satisfies each of the following inequalities.

  1. \(\left| 4x-1 \right|>x-2\),
  2. \(\left| x-2 \right|>x+\left| x \right|\),
  3. \(\sin 2x>\cos x\) for \(0 < x < 2\pi \),
  4. \({{x}^{2}}<{{2}^{x}}\).

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Answer:(a) {x ∈ ℝ}; (b) {x ∈ ℝ: x < 2/3}; (c) {x ∈ ℝ: π/6 < x < π/2 or 5π/6 < x < 3π/2}; (d) {x ∈ ℝ: -0.767 < x < 2 or x > 4}

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