In mathematics, a limit is the value that a function or sequence “approaches” as the input or index approaches some value.^{[1]} Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals.
The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory.
In formulas, a limit is usually written as
and is read as “the limit of f of n as n approaches c equals L“. Here “lim” indicates limit, and the fact that function f(n) approaches the limit L as n approaches c is represented by the right arrow (→), as in
- For example, if
then f(1) is not defined (see division by zero), yet as x moves arbitrarily close to 1, f(x) correspondingly approaches 2
- In other words,
This can also be calculated algebraically, as for all real numbers x ≠ 1.
Now since x + 1 is continuous in x at 1, we can now plug in 1 for x, thus
That means if you want to solve a Limit based question, you have to Factorise given function, then put the value.
You will get your answer…..