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*, thusThat 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…..