Modulus limit complication

[vikcool812]

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 im as h->0 (|h|/h) does not exist , so whats wrong????????

[tiny-tim]

Hi vikcool812! :smile:

(try using the X2 and X2 tags just above the Reply box :wink:)
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 im as h->0 (|h|/h) does not exist , so whats wrong????????

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