Why Does the Limit of |(h² + 4h)|/h Differ When Using Modulus Properties?

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SUMMARY

The limit of |(h² + 4h)|/h as h approaches 0 yields different results based on the method used. When applying the modulus definition, the limit evaluates to 4. However, using the distributive property of modulus leads to a limit of |h|/h, which does not exist as h approaches 0 from the left, resulting in -1. This discrepancy highlights the importance of correctly applying modulus properties in limit calculations.

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vikcool812
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lim as h->0 (|(h^2) + 4h |)/h comes out = 4 when i do it by splitting the definition of function according to modulus , but if according to distributive property of modulus , i can also write it as lim as h->0 (|h|/h)|((h) + 4|)) , but I am as h->0 (|h|/h) does not exist , so what's wrong?
 
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Hi vikcool812! :smile:

(try using the X2 and X2 tags just above the Reply box :wink:)
vikcool812 said:
lim as h->0 (|(h^2) + 4h |)/h comes out = 4 when i do it by splitting the definition of function according to modulus , but if according to distributive property of modulus , i can also write it as lim as h->0 (|h|/h)|((h) + 4|)) , but I am as h->0 (|h|/h) does not exist , so what's wrong?

No, limh->0- |h2 + 4h |/h = -4, just as limh->0- |h|/h = -1.
 

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