Limits

The limit of a function f

The limit of a function f is a real number l as x tends to c if the value of f(x) approaches l as x approaches c. It is written as lim_{x→c} f(x).

If limits of two functions exist

If limits of two functions exist at the same point, then the limit of their sum, difference, product, and quotient can be found using the standard lim

If a lies in the domain

If a lies in the domain of f, then lim_{x→a} f(x) = f(a). This is the easiest method when the function is defined at the point of approach.

When direct substitution gives 0/0

When direct substitution gives 0/0, factorise numerator and denominator, cancel the common factor, and then substitute again. The common factor is oft

For expressions containing square roots

For expressions containing square roots, multiply numerator and denominator by the conjugate to remove the root. This often changes an indeterminate f