Question Detail
Question
What is \( \lim_{h \to 0} \frac{\cos(\frac{\pi}{2} + h) - \cos(\frac{\pi}{2})}{h} \)?
Correct Answer
Option C is the correct answer.
Detailed Explanation
This limit is the definition of the derivative of ( f(x) = \cos x ) evaluated at ( x = \frac{\pi}{2} ). Since ( f'(x) = -\sin x ), then ( f'(\frac{\pi}{2}) = -\sin(\frac{\pi}{2}) = -1 ).
Hint
Identify the limit as the definition of a derivative at a point.