To solve limit problems in Class 11 Maths Chapter 12 (Limits and Derivatives), follow these steps:
1. Substitution: Directly put the given value of $x$.
2. Factorization: Factor and cancel common terms if you get $\frac{0}{0}$.
3. Rationalization: Multiply by the conjugate for roots.
4. Trigonometric Limits: Use identities like $\lim\limits_{x \rightarrow 0} \frac{\sin x}{x}=1$.
5. L'Hôpital's Rule (for indeterminate forms): Differentiate numerator and denominator separately.