   Chapter 2.3, Problem 42E

Chapter
Section
Textbook Problem

Find the limit, if it exists. If the limit does not exist, explain why. lim x → − 6 2 x + 12 | x + 6 |

To determine

To find: The limit of the function limx6(2x+12|x+6|).

Explanation

Definition used:

An absolute function |x| is defined as follows.

|x|={x if x<0x if x0

Direct substitution property:

If f is a polynomial or a rational function and a is in the domain of f, then limxaf(x)=f(a).

Theorem 1:

The limit limxaf(x)=L if and only if limxaf(x)=L=limxa+f(x).

Calculation:

Let f(x)=2x+12|x+6|.

Use the definition of absolute value function to define the function |x+6|,

|x+6|={x+6if x+60(x+6)if x+6<0={x+6if x6(x+6)if x<6

Since f(x)=2x+12|x+6| for x6,

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