Parameters

Number of Terms
4

More terms = better approximation

Error Range
[-2, 2]

Symmetric range around x=0 for error calculation

General Taylor Series

f(x)=∑n=0∞f(n)(0)n!xnf(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!} x^n

Formula for eˣ

ex=∑n=0∞xnn!e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}

Term-by-Term Expansion

ex≈e^x \approx
11
+
xx
+
x22!\frac{x^{2}}{2!}
+
x33!\frac{x^{3}}{3!}
+ ...

Each term is color-coded to match its graph representation above