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Math Asked by a SnapAndSolve user · about 3 hours ago

Find \( \lim_{x \to \frac{1}{2}} \frac{\cos(\pi x)}{x^2 - \sqrt{x}} \). Choose 1 answer: A) \(...

Find \( \lim_{x \to \frac{1}{2}} \frac{\cos(\pi x)}{x^2 - \sqrt{x}} \).
Choose 1 answer:
A) \( \frac{\pi}{2\sqrt{e}} \)
B) \( \frac{1}{2\sqrt{e}} \)
C) \( \frac{\pi}{2} \)
D) The limit doesn't exist.

Answer

Answer: D) The limit doesn't exist.

Explanation: As \( x \to \frac{1}{2} \), the denominator \( x^2 - \sqrt{x} \) approaches zero, and the numerator \( \cos(\pi x) \) oscillates between -1 and 1. This results in an undefined behavior, indicating that the limit does not exist.

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