Question Detail

MTH 102 Limits Objective Question

Question

Evaluate the limit of \( \frac{\ln(\cos 3x)}{\ln(\cos 2x)} \) as \( x \) approaches 0.
Options
A \(\frac{3}{2}\)
B \(\frac{9}{4}\)
Correct Answer
C 1
D 0
Correct Answer

Option B is the correct answer.

Detailed Explanation

Using L'Hospital's rule twice and trigonometric limits, the result is ( \frac{3^2}{2^2} = \frac{9}{4} ).

Hint

Exercise 1.1, Question 28.

Question Info