Limits calculation formulas

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The limit of the constant equals to this constant:

limit of the constant (constant c - constant)

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

limit of the sum

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

limit of the difference

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

limit of the multiplication

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

limit of the division if the condition limit of the g function ≠ 0 is hold

The power function limit:

power function limit (exponent m - natural number)

The root function limit:

root function limit (root index m - natural number)

The main limits

The first wonderful limit:

first wonderful limit (limit variable - angle in radians)

The second wonderful limit:

second wonderful limit

Other useful limits formulas:

limit tg(x)/x as x → 0

limit (1-cos(x))/x as x → 0

limit (1-cos(x))/x^2 as x → 0

limit arcsin(x)/x as x → 0

limit arctg(x)/x as x → 0

limit (arccos(x))^2/(1-x) as x → 0

limit arccos(x^2)/(1-x) as x → 0

limit ((1+x)^alpha-1)/x as x → 0

limit (1+x)^(1/x) as x → 0

limit log(alpha,1+x)/x,x,0) as x → 0

limit ln(1+x)/x as x → 0

limit (a^x-1)/x as x → 0

limit (e^x-1)/x as x → 0

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 by substituted by their equivalents:

limit ln(1+x)/x,x,0 as x → 0

limit sin(x)/x,x,0 as x → 0

пример использования эквивалентности бесконечно малых



To calculate the limits you can use our online calculator.