Question

Find the limit of the function algebraically.

Answer 1

\[\lim_{x \rightarrow0} \frac{ x^2 + 3 }{ x^4 }\]

Answer 2

i wonder what "algebraically" means in this context

Answer 3

I understand that you usually have to factor then plug in, but I see no way to factor this :o

Answer 4

yeah so you can't do it
there is no limit

Answer 5

if the denominator goes to zero, but the numerator does not, then no limit
don't try any further

Answer 6

Oh, I wasn't sure. Thanks c:

Answer 7

yw

Answer 8

@agent0smith see i am right sum of the time

Answer 9

It's 3/0 so infinity... doesn't exist. Don't see how to do it algebraically.

Sumtimes you just can't.

Answer 10

even if you can compute the limit, the word "algebraically" doesn't make sense to me

Answer 11

Sorry its how all the questions are worded. :c

Answer 12

I'd guess it means as opposed to numerically, eg making a table of values


You can break it up into a some of two limits
\[\Large \lim_{x \rightarrow0} \frac{ x^2 + 3 }{ x^4 } = \lim_{x \rightarrow0} \frac{ x^2 }{ x^4 } + \lim_{x \rightarrow0} \frac{ 3 }{ x^4 }\] that's about all you can do algebraically

Answer 13

Other than simplify the some of those two limits sum more \[\Large \lim_{x \rightarrow0} \frac{ 1 }{ x^2 } + \lim_{x \rightarrow0} \frac{ 3 }{ x^4 }\]

Answer 14

No, the lessons refer to factoring before plugging in the value as finding the limit algebraically. Not sure why

Answer 15

Ah. Well then move along, no factoring to see here.