Calculus

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2017 Q.6)** **1. Governing Concept & Definition**: - **Topic**: Engineering Mathematics & Fundamental Trigonometric Limits - Evaluating the canonical limit: $\lim_{x \to 0} \frac{\sin x}{x}$ **2. Detailed Step-by-Step Calculation**: - By L'Hôpital's Rule or Taylor series expansion ($\sin x = x - \frac{x^3}{6} + \dots$): $\lim_{x \to 0} \frac{\sin x}{x} = \lim_{x \to 0} \frac{\cos x}{1} = \frac{\cos 0}{1} = \frac{1}{1} = 1$ **3. Final Answer**: - **Calculated Value**: **1** - **Official GATE Accepted Range**: **1 to 1**