Question
Evaluate the limit:
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nHJXEMtTYG1VFNTEyAOWsymdgKA9N814icqDZ747wPY/HwZnjB+jYGmFDjfysLmwnIY9Al4xVWNz0KMVEaeC+a3OjHzRDAdnl30CorHgbqHTSuaYVPURSLrsPlSNjIygvj4eADAp59+iszMzLltnhipoz/DeGOXLBzVUKLY2NiJofHMzMyHzNkLIVJHf6qeiOiuTmRuqIYKEFhLzal2IkRENVSA2NhY6PX6mW/iEjIDqqEIkRHVUITIiBKKEBlRQhEiI0ooQmRECUWIjCihCJERJRQhMqKEIkRGlFCEyIgSihAZUUIRIqP/B4mlopRttZf5AAAAAElFTkSuQmCC" alt="" />Solution
ATQ,
Factor the numerator xΒ² β 4 = (x β 2)(x + 2) Multiply numerator and denominator by the conjugate of the denominator Multiply by (β(x + 2) + 2) / (β(x + 2) + 2) Denominator becomes: (β(x + 2) β 2)(β(x + 2) + 2) = (x + 2) β 4 = x β 2 Expression becomes: [(x β 2)(x + 2)(β(x + 2) + 2)] / (x β 2) Cancel (x β 2) Remaining expression: (x + 2)(β(x + 2) + 2) Substitute x = 2 (2 + 2)(β(4) + 2) = 4(2 + 2) = 4 Γ 4 = 16
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