Find the limit of the function algebraically.

limit as x approaches zero of quantity negative six plus x divided by x to the fourth power.
Does this limit not exist?:)

Question

Find the limit of the function algebraically.

limit as x approaches zero of quantity negative six plus x divided by x to the fourth power.
Does this limit not exist?:)

anonymous · Answer

attachment

hartnn · Answer

it does exist

hartnn · Answer

the numerator is negative, the denominator is of higher power and positive

anonymous · Answer

does this one not exist too?

hartnn · Answer

the first one exists, the 2nd one doesn't

anonymous · Answer

then how would I find the limit for the first one?:)

hartnn · Answer

the exponent of x in denominator is greater than that in numerator
so it'll be $\pm \infty$
now whether its negative or positive ... ?

hartnn · Answer

the numerator will be negative and denominator will be positive always,
hence
-/+ = -
hence 
$\Large -\infty$

anonymous · Answer

well my answer choices for the first one is 
6
0
-6 
does not exist

hartnn · Answer

it exist and = -infinity
but with the given choices,
fo for does not exist

hartnn · Answer

*go for

hartnn · Answer

so yes, both limits does not exist

anonymous · Answer

thanks love you rock:)