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    Question

    Evaluate the limit:

    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nHJXEMtTYG1VFNTEyAOWsymdgKA9N814icqDZ747wPY/HwZnjB+jYGmFDjfysLmwnIY9Al4xVWNz0KMVEaeC+a3OjHzRDAdnl30CorHgbqHTSuaYVPURSLrsPlSNjIygvj4eADAp59+iszMzLltnhipoz/DeGOXLBzVUKLY2NiJofHMzMyHzNkLIVJHf6qeiOiuTmRuqIYKEFhLzal2IkRENVSA2NhY6PX6mW/iEjIDqqEIkRHVUITIiBKKEBlRQhEiI0ooQmRECUWIjCihCJERJRQhMqKEIkRGlFCEyIgSihAZUUIRIqP/B4mlopRttZf5AAAAAElFTkSuQmCC" 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    A 16 Correct Answer Incorrect Answer
    B 10 Correct Answer Incorrect Answer
    C 25 Correct Answer Incorrect Answer
    D 18 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Factor the numerator x² – 4 = (x – 2)(x + 2) Multiply numerator and denominator by the conjugate of the denominator Multiply by (√(x + 2) + 2) / (√(x + 2) + 2) Denominator becomes: (√(x + 2) – 2)(√(x + 2) + 2) = (x + 2) – 4 = x – 2 Expression becomes: [(x – 2)(x + 2)(√(x + 2) + 2)] / (x – 2) Cancel (x – 2) Remaining expression: (x + 2)(√(x + 2) + 2) Substitute x = 2 (2 + 2)(√(4) + 2) = 4(2 + 2) = 4 × 4 = 16

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