Question

Find the limit of the function algebraically.
lim x^2+2x/x^4
x->0

Answer 1

algebracilly eh, divide top and bottom by x^4

Answer 2

I've tried it a million times but I always get zero in the denominator. I think my teacher wants me to find one without a zero as the denominator.

Answer 3

or is this something to do with "first princilpes" of derivatives

Answer 4

Yes it deals with derivatives.

Answer 5

.... then you are in for a nightmare lol

Answer 6

\[\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}\]

Answer 7

i hear that sometimes:

f(b)-f(a)
------ is simpler
b-a

Answer 8

Ah I don't know if I must use that expression for this question but I'll give it a try.

Answer 9

Yeah, definitely not how I am supposed to be doing it hahah. Thank you though @amistre64

Answer 10

\[\frac{x^{2}+2x}{x^{4}} = \frac{x(x+2)}{x^{4}} = \frac{x+2}{x^{3}}\]
\[\lim_{x \rightarrow 0} \frac{x+2}{x^{3}} = \lim_{x \rightarrow 0} \frac{2}{0}=\infty\]

Answer 11

Yes okay good I figured there is no way to make the denominator anything other than zero but I wasn't sure. Thank you so much for confirming it! @dumbcow

Answer 12

yw

Answer 13

Doe that mean it is zero, or that it does not exist?

Answer 14

*Does

Answer 15

well, infinity is not zero, so it aint zero. so it depends on how the course defines a divide by zero. DNE is fine for some classes, and infinity is fine for others.

Answer 16

DOES NOT EXIST