There aren't many direct applications of limits, but limits are used in other mathemathical branches such as **infinitesimal calculus** (derivations and integrals are defined as special limits of functions see e.g. *Bartle, Sherbert*:* Introduction to Real Analysis*). **Calculating infinite sums** (like Taylor or Fourier series), **calculating limit of convergent matrix** (which can be important for random process such as Markov chain), **asymptotic analysis** (which is important in design and analysis of algorithms see e.g. *Knuth: The Art of Computer Programming vol. 1*), **finding convergece rate** (important for design and analysis of numerical algorithms e.g. Newton method has superlinear convergence rate while Brent's has linear convergence rate which means that Newton's method is faster.), **convergence of random variables** (very important in probability theory and statistics adn as such in economics see e.g. Mittelhammer: Mathematical Statistics for Economics and Business).

Hope this helps.

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