Question

Find the limit algebraically as x approaches zero of the function (-6 + x) / x^4 .

Answer 1

Start by plugging in \(x = 0\) and you will see that this amounts to \(\dfrac{-6}{0}\)

Dunno how much formalism you require, but then you can break it out as follows:

\(\lim\limits_{x \to 0} \dfrac{-6 + x}{x^4} = \dfrac{\lim\limits_{x \to 0} -6 + x}{\lim\limits_{x \to 0} x^4} = \dfrac{ -6 }{\lim\limits_{x \to 0} x^4}\)


Checking for **two-sidedness**, as otherwise you do not have a limit as such, note the denominator is always +ve. That should do it.

Answer 2

@sweetburger

you can't do that (the second part)

Answer 3

I realize my mistake. Sorry about that. Not trying to lead anyone the wrong way.