Indeterminate form

Expression in mathematical analysis

In calculus, it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function. For example, lim x → c ( f ( x) + g ( x)) = lim x → c f ( x) + lim x → c g ( x) , lim x → c ( f ( x) g ( x)) = lim x → c f ( x) ⋅ lim x → c g ( x) , {\displaystyle {\begin{aligned}\lim _{x\to c}{\bigl (}f(x)+g(x){\bigr)}&=\lim _{x\to c}f(x)+\lim _{x\to c}g(x),\\[3mu]\lim _{x\to c}{\bigl (}f(x)g(x){\bigr)}&=\lim _{x\to c}f(x)\cdot \lim _{x\to c}g(x),\end{aligned}}} and likewise for other arithmetic operations; this is sometimes called the algebraic limit theorem. However, certain combinations of particular limiting values cannot be computed in this way, and knowing the limit of each function separately does not suffice to determine the limit of the combination.

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