Define indeterminate form of a function

A limit lim_{x→a} f(x) is said to be in an indeterminate form when direct substitution of x = a gives an expression whose value cannot be decided, so the limit may be any number or may not exist, and further work is needed.

The seven standard indeterminate forms are:

0/0,  ∞/∞,  0·∞,  ∞ − ∞,  1^∞,  0⁰,  ∞⁰

Example: lim_{x→0} (sin x)/x gives 0/0 on substitution but its value is 1.

The forms 0/0 and ∞/∞ are evaluated by L'Hospital's rule. The other forms are first rewritten as 0/0 or ∞/∞: 0·∞ by writing f·g = f/(1/g), ∞ − ∞ by taking a common denominator, and 1^∞, 0⁰, ∞⁰ by taking logarithms.