It is important to understand the concept of limits because it will be present in many calculus problems. Limit shows us how some value has limit in f(y) if the f(x) approaches that value. For instance, if we have a limit that will be when X goes to zero; y goes to 1.

## Instructions

1) Write down the equation for the function.

For example:

y = f(x) = ( x^2 -2x +3 ) / ( x – 3 )

2) Set up the limit which includes the value that x approaches

From the example:

LIM [ ( x^2 -2x +3 ) / ( x - 3 ) ]

(x -> +3 )

3) Factorize and reduce the function. Algebraic methods should be used here.

( x^2 -2x +3 ) / ( x – 3 ) =

[ ( x + 1) ( x - 3 ) ] / ( x – 3 ) =

( x + 1 )

4) Replace the expression which is reduced on the limit. Solving the limit. You will do this if replace the value of the variable ( x ) with the value it approaches ( x -> +3, replace “x” with +3).

LIM [ ( x + 1 ) ]

(x -> +3 )

( +3 +1 ) = 4

LIM [ ( x + 1 ) ] = 4

(x -> +3 )

## Tips and warnings

When you solve limit problems you must be sure that you didn’t end with qualities that are not defined. You will have undefined quantity if you divide any of your expressions by zero. You will prevent undefined values if you factorize and reduce those expressions.