Finite Limit
\(\lim_{x \to 2} x^2 = 4\)
Limit Calculator
Calculate limits of functions at specific points or infinity with step-by-step solutions
Tulokset
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Theory & Formula
A limit describes the behavior of a function as its input approaches a particular value. It's fundamental to calculus and analysis.
Key Concepts
- Direct Substitution \(\lim_{x \to a} f(x) = f(a)\)
- One-Sided Limits (\(x \to a^-\)) ja (\(x \to a^+\)) peavad kokku langema
- Limits at Infinity \(x \to \pm\infty\)
- Indeterminate Forms \(\frac{0}{0}, \frac{\infty}{\infty}\)
- Squeeze Theorem \(g(x) \le f(x) \le h(x)\) ja \(\lim g(x) = \lim h(x) = L\), siis \(\lim f(x) = L\)
Worked Examples
Limit at Infinity
\(\lim_{x \to \infty} \frac{1}{x} = 0\)
Discontinuity
\(\lim_{x \to 0} \frac{1}{x} \text{ does not exist}\)