Question

The limit of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:

• A. \( 1 \)
• B. \( 0 \)
• C. \( \infty \)
• D. Does not exist

Hint:

Remember that \( \lim_{x \to 0} \frac{\sin x}{x} = 1 \) is a standard result in calculus that you should know.

Answer 1

The Correct Option is A

The objective is to determine the limit \( \lim_{x \to 0} \frac{\sin x}{x} \). Step 1: Cite a fundamental limit The limit \( \lim_{x \to 0} \frac{\sin x}{x} = 1 \) is a foundational result in calculus. Step 2: Finalize the determination Consequently, the limit evaluates to: \[ \lim_{x \to 0} \frac{\sin x}{x} = 1 \] Answer: The limit's value is \( 1 \), corresponding to option (1).