Question

Find the limit of the function algebraically.
lim x goes to 0 (x^2+2x)/(x^4)

Answer 1

\[\lim_{x \rightarrow 0}\frac{x^2+2x}{x^4}\]
You could factor out an x on top and and x on bottom

Answer 2

so \[\lim (x+2)/x^3\]

Answer 3

what happens when you plug in 0

Answer 4

you get 0

Answer 5

0+2 isn't 0

Answer 6

2/0 = 0

Answer 7

2/0 is not 0

Answer 8

the only thing that can possibly make a fraction 0 is the top

Answer 9

if the top is not 0, then you definitely know the fraction is never 0

Answer 10

undefined

Answer 11

oh

Answer 12

and if you have 0/0 then that would be indeterminate form
but we have 2/0 which is undefined or does not exist

Answer 13

0/0 means you have to do more work
2/0 means you are done
0/2 would be 0

Answer 14

alright, thanks for explaining that to me

Answer 15

np