Question

When do i know what limit test to use and what are the steps?

Answer 1

all the texts that ive come across say its a matter of trial and error. If one method produces undetermined results, try another.

Answer 2

hm alright iv seen a lot of times where people take the highest power and just leave the coefficient when can i do that? and when do i divided by the highest power in the numerator?

Answer 3

are you refering to rational expressions, such that the top and bottom are polynomials?

Answer 4

if so, the highest degree always takes control for large values of x; if its up top, we grow beyond bounds, if its on the bottom, we diminish to zero

but what if the highest degree is equal on top and bottom? then they essential cancel each other out and you remain with their leading coefficinets

Answer 5

but when the limit goes to infinity doesnt that make it infinity over infinity thus using the L'Hospital Rule

Answer 6

highest on top
\[\lim_{x\to inf}\frac{x^3}{x}=\infty\]

highest on bottom
\[\lim_{x\to inf}\frac{x^2}{x^5}=0\]

top equals bottom
\[\lim_{x\to inf}\frac{2x^3}{5x^3}=\frac{2}{5}\]

Answer 7

im unclear of the context of your question. can you be more specific as to what limits you are talking about? you mentioned higher degrees, but then suggest Lhop.

Answer 8

if you are still refering to the polynomials, as what i presented. Lhop will work for those.

notice the first one, the bottom derives to 0 first suggesting an undefined limit

notice the second one, the top derives to 0 first suggesting a zero limit

notice the third one, the top and bottom derives to constants at the same time, by simplfying (canceling out all the like factors that the exponents poped out), we are left with the leading coeffs still

Answer 9

alright for example the second on x^2/X^5 when x is approaching inifinity dont you use Lhop, then itll be 2x/5x then use it again and you get 2/5?

Answer 10

only if you want to make up your own rules for derivatives :)

Answer 11

x^2
2x
2
0

x^5
5x^4
20x^3
60x^2

0/60x^2 = 0

Answer 12

a smaller degree will always zero out before a larger degree

Answer 13

oh wow yeah i see, dumb mistake on my part

Answer 14

thanks alot home fly, im not sure whats the limit of questions i can ask in this forum

Answer 15

if you have questions related to a particular post youve made already, its best to keep the conversation going inside that post

if you have a new question, its best to post it up on the left

and there is no limit to the number of questions you can ask, as long as your goal is to learn.

Answer 16

ok i have another question
how does b of n = 1/n diverge?