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Limits involving absolute values often involve breaking things into cases. Remember that |f(x)|= (a) Determine the particle's speed (speed is defined as the absolute value of velocity) at π seconds. (b) Is the particle moving towards or away from the A handbook for solving limits in calculus 1. Case 2: when we deal with a function which has an absolute value term and the limit point. 2.3 Limits Involving Absolute Value. Recall that a function involving absolute value can be expressed as a piecewise-defined function. For example,. One of the most used functions in mathematics is the absolute value function. Its definition and some of its properties are given below. Absolute Value FunctionThe limit of a constant times a function is equal to the constant times the The absolute value of a number indicates its distance from another number. equations and inequalities containing expressions that implement the absolute value function. Table of Contents. 4.1. Piecewise-Defined Functions . Evaluate each limit. 4x+4. 1) lim x+1 = 4. 14 x--11.