Série de Maclaurin eˣ (5 termos)

The Maclaurin Series calculator for eˣ approximates the exponential function using the first 5 terms: 1 + x + x²/2! + x³/3! + x⁴/4!. Simply enter a value for x, and the tool computes the sum of these terms, providing a quick approximation of eˣ without using complex exponential functions. Ideal for calculus students wanting to see how Taylor series work in practice.

How it works: for a given x, the calculator computes each term separately (x^0/0!, x^1/1!, x^2/2!, x^3/3!, x^4/4!) and sums them. The result is a degree-4 polynomial approximation to eˣ. The smaller the x value, the more accurate the approximation, as higher-order terms become negligible. The tool uses basic arithmetic with precomputed factorials, no recursion or infinite loops.

Use this calculator in educational settings, such as numerical calculus or power series classes. For example, for x = 1, the result approximates e ≈ 2.70833 (actual value: 2.71828). It is also useful for quick manual checks of eˣ in physics or engineering problems. Remember that with only 5 terms, the approximation is reasonable only for |x| ≤ 1; larger values require more terms.

Important caveats: the Maclaurin series expands around x = 0, so accuracy decreases as x moves away from zero. Do not use this approximation for high-precision calculations, such as in finance or statistics, without error checking. For negative x, the series alternates signs and may converge more slowly. Always compare with the actual eˣ value if available.