Subjects calculus

Limit Sin Over T C6B064

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1. **Problem:** Evaluate the limit $$\lim_{t \to 0} \frac{\sin t}{t}$$ using special limits. 2. **Formula and important rule:** The special limit $$\lim_{x \to 0} \frac{\sin x}{x} = 1$$ is fundamental in calculus. 3. **Step-by-step solution:** 1. Recognize that the limit matches the special limit form directly. 2. Therefore, $$\lim_{t \to 0} \frac{\sin t}{t} = 1$$. 4. **Explanation:** This limit is a standard result that helps evaluate many trigonometric limits. It states that as the angle approaches zero, the ratio of sine of the angle to the angle itself approaches 1. **Final answer:** $$1$$