Question Detail
Question
Evaluate lim(x→0) (√(x+9)-3)/(2x)
Correct Answer
Option D is the correct answer.
Detailed Explanation
Rationalise by multiplying by (√(x+9)+3): the numerator becomes x, giving x/[2x(√(x+9)+3)] = 1/[2(√(x+9)+3)], which at x=0 gives 1/12.
Hint
Multiply numerator and denominator by the conjugate √(x+9)+3.