Standard limits and equivalent functions

Some fundamental limits — such as $\lim_{x\to 0}\frac{\sin x}{x}=1$ — come up again and again and must be known by heart: these are the standard limits. From them one derives a list of equivalent functions, approximations that can be substituted inside a limit to simplify calculations, provided their conditions of use are respected.

• Standard limits
• Equivalent functions
• Examples with equivalent functions