Table Of Limits

LIMITS FOR GENERAL FUNCTIONS

:

\mbox{If }\lim_{x 	o c} f(x) = L_1 \mbox{ and }\lim_{x 	o c} g(x) = L_2 \mbox{ then:}

= L_1 \pm L_2

\lim_{x 	o c} \,

{Link without Title} = L_1 imes L_2

::

\lim_{x 	o c} rac{f(x)}{g(x)} = rac{L_1}{L_2} \qquad \mbox{ if } L_2 
e 0

\lim_{x 	o c} \, f(x)^n = L_1^n \qquad \mbox{ if }n \mbox{ is a positive integer}

\lim_{x 	o c} \, f(x)^{1 \over n} = L_1^{1 \over n} \qquad \mbox{ if }n \mbox{ is a positive integer, and if } n \mbox{ is even, then } L_1 > 0

NEAR INFINITIES

\lim_{x	o\infty}N/x=0 \mbox{ for any real N}

\lim_{x	o\infty}x/N=\begin{cases} \infty, & N > 0 \ \mbox{does not exist}, & N = 0 \ -\infty, & N < 0 \end{cases}

\lim_{x	o\infty}x^N=\begin{cases} \infty, & N > 0 \ 1, & N = 0 \ 0, & N < 0 \end{cases}

\lim_{x	o\infty}N^x=\begin{cases} \infty, & N > 1 \ 1, & N = 1 \ 0, & N < 1 \end{cases}

\lim_{x	o\infty}N^{-x}=\lim_{x	o\infty}1/N^{x}=0 \mbox{ for any } N > 1

\lim_{x	o\infty}\sqrt

{Link without Title} {N}=\begin{cases} 1, & N > 0 \ 0, & N = 0 \ \mbox{does not exist}, & N < 0 \end{cases}

\lim_{x	o\infty}\sqrt

{Link without Title} {x}=\begin{cases} 1, & N > 0 \ (-1..1), & N = 0 \ -1, & N < 0 \end{cases}

\lim_{x	o\infty}\log x=\infty

\lim_{x	o0^+}\log x=-\infty

	CATEGORIES ABOUT TABLE OF LIMITS

	calculus

	mathematics-related lists

	limits

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