In mathematics, a limit is the value that a function or sequence “approaches” as the input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals.
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…..