Operations of Limits
There are several functions in mathematics, which are formed in various types of combinations by two or more basic functions. Actually, those functions are mainly formed by math operations, and the limits of such functions should be evaluated in calculus. In fact, it is really complicated to find limits of such functions. So, we require some special limit formulas to find the limits of them and they are called the fundamental operations with limits.
Basic operations
There are four fundamental operations on limits. So, let’s learn each limit operation rule with proof and also learn how to use each limit operation’s formula with understandable examples.
$\displaystyle \large \lim_{x\,\to\,a}{\normalsize \Big[f(x)+g(x)\Big]}$
$\displaystyle \large \lim_{x\,\to\,a}{\normalsize \Big[f(x)-g(x)\Big]}$
$\displaystyle \large \lim_{x\,\to\,a}{\normalsize \Big[f(x) \times g(x)\Big]}$
$\displaystyle \large \lim_{x\,\to\,a}{\normalsize \Big[f(x) \div g(x)\Big]}$
Other operations
There are two other math operations in limits additionally. Now, let’s know both of them with proofs and also learn how to use the math operations with limits while solving the problems in calculus.
$\displaystyle \large \lim_{x\,\to\,a}{\normalsize \dfrac{1}{f(x)}}$
$\displaystyle \large \lim_{x\,\to\,a}{\normalsize {f(x)}^{\displaystyle g(x)}}$
Once you clearly learned all the limits’ operations, then you are ready to practice them in limits problems.