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Question

Evaluate the limit:

A 16 Correct Incorrect

B 10 Correct Incorrect

C 25 Correct Incorrect

D 18 Correct Incorrect

Detailed 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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