How to Find the Limit of a Function in Calculus

The concept of limit is central to understanding most of calculus' concepts. In short, a limit returns the value approached by a function output ( y ), when the function's input ( x ) approaches a value. For example, a limit would be when x approaches zero; y approaches one. Although this idea seems to be very simple, the idea of approaching a value but never reaching it is complex and advanced. Calculating the limit of a function is a great exercise to get acquainted with the basis of calculus.

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 with the value approached by the input "x".

      From the example:

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

      (x -> +3 )

    • 3

      Factorize and reduce the function as much as possible. Use factorization and algebraic methods.

      ( x^2 -2x +3 ) / ( x - 3 ) =

      [ ( x + 1) ( x - 3 ) ] / ( x - 3 ) =

      ( x + 1 )

    • 4

      Replaced the reduced expression on the limit. Solve the limit by replacing 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 )

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