Question Detail
Question
Evaluate the limit of \( \frac{8^x - 2^x}{4x} \) as \( x \) tends to 0.
Correct Answer
Option C is the correct answer.
Detailed Explanation
Using L'Hospital's rule: ( \frac{8^x \ln 8 - 2^x \ln 2}{4} ). At ( x=0 ), ( \frac{\ln 8 - \ln 2}{4} = \frac{\ln 4}{4} = \frac{1}{4} \ln 4 ).
Hint
Exercise 1.1, Question 33.