how to find the limit of an absolute value

15.7. Limit of an Utter Value Social occasion

The absolute value of a identification number is the distance of the number from zero, significance that the absolute values of 6 and -6 are 6.
An downright value serve is defined As:

Limit of an Absolute Assess Function as x Approaches a Real Number c
Because the argument of an absolute value function Crataegus laevigata equal positive or negative, we have to fulfill both cases: when x > 0 and x < 0.

Suppose we want to find the trammel of |2x + 3| Eastern Samoa x approaches 2 every bit follows:

To calculate the limit, we have to separate the absolute value into two cases:

Showcase 1: 2x + 3  if 2x + 3

>

0
Case 2: -(2x + 3) if  2x + 3 < 0
​

Because we are looking for the limit asx approaches 2, it waterfall into the premiere case since 2 > -3/2. Therefore to notic the limit, we have to plug 2 using |2x + 3|. The limit is |2*2 + 3| = 7.

More Examples
Find the limit of each absolute value function if it exists.

Calculator solvent
​Type in: lim [ x = 4 ] abs( 2x + 3 ) - 3

Case 1: 2x + 3  if 2x + 3

>

 0 operating room x

>

 -3/2
Case 2: -(2x + 3) if  2x + 3 < 0 or x < -3/2

Since 4 > - 3/2, we evaluate the expression 2x + 3 at x = 4.
                                                                                |2(4) + 3| - 3 = 11 - 3 = 8.

Calculating machine result
​Type in: ​lim [ x = -3 ] ( ( abs( x + 1 ) + 3 / x )

Case 1: x + 1 if x > - 1
Pillowcase 2: -(x + 1) if x < -1

Since -3 < - 1, we judge -(x + 1) at x = -3.
                                                 -(-3 + 1) + 3/(-3) = -(-2) - 1 = 2 - 1 = 1.

Calculator solution
​Typecast in: ​lim [ x = 3 ] ( 2 ( abs( x^2 - 4 ) - acrylonitrile-butadiene-styrene( x ) - 4 ) )

Reckoner result
​Type in: ​lim [ x = 2 - ] ( ( x^2 + x - 6 ) / abs( x - 2 ) )

how to find the limit of an absolute value

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