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

[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 I am as h->0 (|h|/h) does not exist , so what's wrong?

 

[tiny-tim]

Hi vikcool812!

(try using the X² and X₂ tags just above the Reply box )

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, lim_h->0- |h² + 4h |/h = -4, just as lim_h->0- |h|/h = -1.