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1.
$\lim{x \to \infty} \left(1+\dfrac{1}{x}\right)^x=e$
E
Limit
2.
$\lim{x\to\infty}\left(1-\dfrac{1}{x}\right)^x=\dfrac{1}{e}$
Limit
E
3.
$\lim{x \to 0}\left(1+x\right)^\frac{1}{x} = e$
E
Limit
4.
$\lim{x \to 0}\left(1+kx\right)^\frac{m}{x}=e^{km}$
E
Limit
5.
$\lim {x \to \infty}\left(\dfrac{x}{x+k}\right)^x=e^{-k}$
E
Limit
6.
$\lim{x \to \infty} \dfrac{x}{e^x} = 0$
E
Limit
7.
$\lim{x \to 0} \left(\dfrac{e^x-1}{x}\right) = 1$
E
Limit
8.
$\lim {x \to 0} \left(\dfrac{e^{ax}-1}{x}\right)=a$
E
Limit
9.
$\lim{x \to \infty}\left(1+\dfrac{k}{x}\right)^{mx}=e^{km}$
E
Limit
10.
$\int e^x dx = e^x + C$
E
Indefinite Integral
11.
$ \int x e^{ax}dx = \dfrac{e^{ax}}{a^2}(ax-1)+C $
E
Indefinite Integral
12.
$\int e^{ax} \sin bx dx = \dfrac{a\sin bx - b \cos bx}{a^2+b^2} e^{ax} + C $
E
Exponents
Indefinite Integral
Trigonometry
13.
$\int e^{ax} \cos bx dx = \dfrac{a\cos bx - b \sin bx}{a^2+b^2} e^{ax} + C $
E
Indefinite Integral
Trigonometry

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