Limits calculation formulas

The limit of the constant equals to this constant:

limxacc (c - constant)

The limit of the sum equals to the sum of the limits:

limxafxgxlimxafxlimxagx

The limit of the difference equals to the difference of the limits:

limxafxgxlimxafxlimxagx

The limit of the multiplication equals to the multiplication of the limits:

limxafxgxlimxafxlimxagx

The limit of the division equals to the division of the limits:

limxafxgxlimxafxlimxagx if the condition limxagx0 is hold

The power function limit:

limxafxmlimxafxm (m - natural number)

The root function limit:

limxamfxmlimxafx (m - natural number)

The main limits:

The first wonderful limit:

limx0sinxx1 (x - angle in radians)

The second wonderful limit:

limx11xxe

Other useful limits formulas:

limx0tgxx1
limx01cosxx0
limx01cosxx212
limx0arcsinxx1
limx0arctgxx1
limx1arccos2x1x2
limx01xα1xα
limx01x1xe
limx0logα1xxlogαe
limx0ln1xx1
limx0ax1xlna
limx0ex1x1

infinitesimal

Infinitesimal equivalence:

As x → 0 , the following functions are equivalent:

x ~ sin(x) ~ arcsin(x) ~ tg(x) ~ arctg(x) ~ ln(1+x)

To find the limit of the division of two infinitesimal functions, they can be substituted by their equivalents:

limx0ln1xxlimx0xx1

limx0sinxxlimx0xx1

limx0sinxx2x42xx3sinxx2x4~x2xx3~2xlimx0x2x12

To calculate the limits you can use our online calculator.

Other useful links:

Definite integral online calculator
Series sum calculator

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