Limits serve as the gateway to all of calculus, and understanding them deeply pays dividends across multiple JEE topics.

Connection to Derivatives: The derivative f'(a) = lim(h->0) [f(a+h) - f(a)]/h is itself a limit. The standard limit $\frac{x^n - a^n}{(x - a)}$ -> n*a^(n-1) IS the power rule. L'Hopital's Rule uses derivatives to evaluate limits, creating a circular but powerful connection.

Connection to Integration: Definite integrals are limits of Riemann sums: integral from a to b of f(x)dx = lim(n->inf) sum f($x_i$)*$delta_x$. The Riemann sum conversion technique (recognizing $\frac{1}{n}$*sum f$\frac{r}{n}$ as an integral) directly uses this connection.

Connection to Series: Taylor/Maclaurin series are infinite sums that converge to functions within their radius of convergence. The ability to expand functions as power series is one of the most powerful limit-evaluation techniques.

Connection to Differential Equations: Continuity conditions determine where solutions to ODEs exist and are unique (by the existence-uniqueness theorem).

Cross-topic JEE Questions: JEE frequently combines limits with:

• Definite integrals (Riemann sums)
• Derivatives (L'Hopital, derivative definition)
• Sequences and series (convergence tests)
• Curve sketching (asymptotes via limits at infinity)

Mastering limits thoroughly provides a strong foundation for approximately 30-40% of the JEE mathematics syllabus.