A limit is a mathematical computation that tells us the value assumed by a mathematical expression/function as the independent variable approaches a certain value.
Let a function `f(x`) be defined in an open interval in the neighborhood of the number "a".
If as `x` approaches "a" from both left and right sides of "a", `f(x`)approaches a specific number "L" then "L" is called the limit of `f(x)` as `x` approaches a.
Limit is expressed as follows:
`Lim_(x->a) f(x) = L `
And is read as "Limit of `f(x)` as `x-> `a is L" .
Under this definition of the limit of a function, we can categorize limits into these three types:
There are some fundamental theorems on Limits of functions. We present their brief statements here.
In Calculus, many a times there comes a situation where putting the value of `x` gives us an expression of the form `( 0 )/( 0 )` .When such a situation arises, we use simplification method to factorize both the numerator and denominator expressions to see if there is a factor common to both. If such a common factor does occur, we cancel them about and are usually left with an expression in which putting the limit does not give us ` ( 0 )/( 0 ) ` form. We have presented some of the examples of such a scenario here:
In evaluating limits at infinity, we divide both the numerator and the denominator terms by the highest power of variable that appears in the denominator and then put the limit in the new formed expression.