Well-known limits

sin x / x, (1 + 1/n)ⁿ, (eˣ − 1)/x, x ln x and about 50 more, each with the method, L'Hôpital steps and a table of values closing in.

All limits

$\lim_{x \to 0} \frac{\sin\left(x\right)}{x}$
$\lim_{x \to 0} \frac{\tan\left(x\right)}{x}$
$\lim_{x \to 0} \frac{1 - \cos\left(x\right)}{x^{2}}$
$\lim_{x \to 0} \frac{1 - \cos\left(x\right)}{x}$
$\lim_{x \to 0} \frac{e^{x} - 1}{x}$
$\lim_{x \to 0} \frac{\ln\left(1 + x\right)}{x}$
$\lim_{x \to 0} \frac{\arctan\left(x\right)}{x}$
$\lim_{x \to 0} \frac{\arcsin\left(x\right)}{x}$
$\lim_{x \to 0} \frac{e^{x} - 1 - x}{x^{2}}$
$\lim_{x \to 0} \frac{\tan\left(x\right) - \sin\left(x\right)}{x^{3}}$
$\lim_{x \to 0} \frac{\sin\left(x\right) - x}{x^{3}}$
$\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^{x}$
$\lim_{x \to 0} \left(1 + x\right)^{\frac{1}{x}}$
$\lim_{x \to \infty} \left(1 + \frac{2}{x}\right)^{x}$
$\lim_{x \to \infty} \left(1 + \frac{3}{x}\right)^{x}$
$\lim_{x \to \infty} \left(1 - \frac{1}{x}\right)^{x}$
$\lim_{x \to 0^{+}} x \ln\left(x\right)$
$\lim_{x \to 0^{+}} x^{x}$
$\lim_{x \to \infty} x^{\frac{1}{x}}$
$\lim_{x \to \infty} \frac{\ln\left(x\right)}{x}$
$\lim_{x \to \infty} \frac{x}{e^{x}}$
$\lim_{x \to \infty} \frac{x^{2}}{e^{x}}$
$\lim_{x \to \infty} \frac{\sin\left(x\right)}{x}$
$\lim_{x \to \infty} \sqrt{x^{2} + x} - x$
$\lim_{x \to \infty} \sqrt{x + 1} - \sqrt{x}$
$\lim_{x \to 1} \frac{x^{2} - 1}{x - 1}$
$\lim_{x \to 0} x \sin\left(\frac{1}{x}\right)$
$\lim_{x \to 0} \sin\left(\frac{1}{x}\right)$
$\lim_{x \to 0} \frac{\sin\left(2 x\right)}{x}$
$\lim_{x \to 1} \frac{x^{2} - 1}{x - 1}$
$\lim_{x \to 0} \frac{\left(1 + x\right)^{2} - 1}{x}$
$\lim_{x \to 0} \frac{\sin\left(3 x\right)}{x}$
$\lim_{x \to 1} \frac{x^{3} - 1}{x - 1}$
$\lim_{x \to 0} \frac{\left(1 + x\right)^{3} - 1}{x}$
$\lim_{x \to 0} \frac{\sin\left(4 x\right)}{x}$
$\lim_{x \to 1} \frac{x^{4} - 1}{x - 1}$
$\lim_{x \to 0} \frac{\left(1 + x\right)^{4} - 1}{x}$
$\lim_{x \to 0} \frac{\sin\left(5 x\right)}{x}$
$\lim_{x \to 1} \frac{x^{5} - 1}{x - 1}$
$\lim_{x \to 0} \frac{\left(1 + x\right)^{5} - 1}{x}$
$\lim_{x \to 0} \frac{\sin\left(6 x\right)}{x}$
$\lim_{x \to 1} \frac{x^{6} - 1}{x - 1}$
$\lim_{x \to 0} \frac{\left(1 + x\right)^{6} - 1}{x}$
$\lim_{x \to 0} \frac{2^{x} - 1}{x}$
$\lim_{x \to 0} \frac{3^{x} - 1}{x}$
$\lim_{x \to 0} \frac{5^{x} - 1}{x}$
$\lim_{x \to 0} \frac{10^{x} - 1}{x}$