All Maths Formulas

Algebra

$\text{If } \lim_{x \to a} f(x) = l \text{ and } \lim_{x \to a} g(x) = m \text{ ,then}$

lim x \to a [f (x) \pm g (x)] = l \pm m

$\lim_{x \to a} ~\left[ f(x) \pm g(x) \right] = l \pm m$

lim x \to a [f (x) \cdot g (x)] = l \cdot m

$\lim_{x \to a} ~\left[ f(x) \cdot g(x) \right] = l \cdot m$

lim x \to a f ( x ) g ( x ) = l m

$\lim_{x \to a} \frac{f(x)}{g(x)} = \frac{l}{m}$

lim x \to a c \cdot f (x) = c \cdot l

$\lim_{x \to a} c\cdot f(x) = c \cdot l$

lim x \to a 1 f ( x ) = 1 l

$\lim_{x \to a} \frac{1}{f(x)} = \frac{1}{l}$

lim x \to \infty (1 + 1 n) n = e

$\lim_{x \to \infty}~\left(1+\frac{1}{n}\right)^n = e$

lim x \to \infty (1 + n) 1 / n = e

$\lim_{x \to \infty}~(1 + n)^{1/n} = e$

lim x \to 0 sin x x = 1

$\lim_{x \to 0}~\frac{\sin x}{x} = 1$

lim x \to 0 tan x x = 1

$\lim_{x \to 0}~\frac{\tan x}{x} = 1$

lim x \to 0 cos x - 1 x = 0

$\lim_{x \to 0}~\frac{\cos x-1}{x} = 0$

lim x \to a x n - a n x - a = n a n - 1

$\lim_{x \to a}~\frac{x^n - a^n}{x-a} = n\,a^{n-1}$

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