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10 cards from this deck
Infinite series summing to a finite value
f(0)+xf′(0)+x22!f′′(0)+…f(0) + xf'(0) + \frac{x^2}{2!}f''(0) + \ldotsf(0)+xf′(0)+2!x2f′′(0)+…
All real values of xxx
−1<x<1-1 < x < 1−1<x<1 (for n∈Rn \in \mathbb{R}n∈R)
ln(0)=−∞\ln(0) = -\inftyln(0)=−∞, not finite
x−x22+x33−x44+…x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \ldotsx−2x2+3x3−4x4+…
Only multiply terms up to required power of xxx
00\frac{0}{0}00 or ∞∞\frac{\infty}{\infty}∞∞
limf(x)g(x)=limf′(x)g′(x)\lim \frac{f(x)}{g(x)} = \lim \frac{f'(x)}{g'(x)}limg(x)f(x)=limg′(x)f′(x)
(2x)rr!\frac{(2x)^r}{r!}r!(2x)r or 2rxrr!\frac{2^r x^r}{r!}r!2rxr
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