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Calculus/calculus diferrentiation

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Expert: - 5/29/2008


Question
QUESTION: evaluate

lim    (|x - 4|) / x-4
x-4

ANSWER: I almost didn't answer this - that's because there is no answer!  (tee hee hee...)

But seriously, the lim x->4 by decreasing 1 and the lim x->4 by increasing is -1.  Since the upper limint and lowere limits are different, there is no answer -  a better way might be to say that the answer is undefined.

---------- FOLLOW-UP ----------

QUESTION: please elaborate on the meaning of  absolute and  their working. on  reference  to the question i posted:

QA: QUESTION: evaluate

lim    (|x - 4|) / x-4
x-4  

Answer
The absolute value is the positve value:
Examples: |1|=1, |-4.6|=4.6, |5.02|=5.02, |-565/3|=565/3.

|x-4|=x-4 if x>=4 or 4-x if x<4.

Any value of x>4 has the result of |x-4|/(x-4) equal to 1,
any value of x<4 has the result of |x-4|/(x-4) equal to -1, and
at the value x=4, the value is 0/0 (which is undefined),
therefore the limit as x approaches 4 is undefined.

Calculus

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