Question

Limit question from calculus. Problem in comments

Answer 1

divide top and bottom by n^3

Answer 2

After I do that what do I do next?

Answer 3

well pretend n is a really large number... what does the expression equal?

Answer 4

0? Is it nonexistant?

Answer 5

no... are you in precalculus or calculus?

Answer 6

it's a good idea to get a feeling for intuition here

Answer 7

calculus lol. I'm taking an online course and I have no idea what I'm doing

Answer 8

you're looking at
\(\Huge \frac{3-5/n^2}{1-2/n+1/n^3}\) as n becomes really large

Answer 9

that's what you get after you divide both sides by n^3

Answer 10

Yeah I get that but I have to pick one of those answers

Answer 11

if you're going to always worry about which answer to pick you'll have a lot of answers to pick for your course...
honestly if you wanted the answer you could've just looked it up on wolfram alpha

Answer 12

anyways you're interested in what happens when n becomes really, really big

Answer 13

But I want to understand how to do it while getting the right answer.

Answer 14

so when n becomes really really big, some of the terms in that rational expression don't matter...

Answer 15

can you identify which ones?

Answer 16

by don't matter I mean that they approach zero.

Answer 17

The denominator numbers?

Answer 18

well, let's try it out. Let's take n=1 first

Answer 19

\(\Huge \frac{3-5/n^2}{1-2/n+1/n^3}\)

Answer 20

-2/0 is what I got

Answer 21

\(\Huge \frac{3-5/1^2}{1-2/1+1/1^3}\)=(3-5)/(1-2+1)=-2/((0)=undef

Answer 22

let's try it for n=10

Answer 23

\(\Huge \frac{3-5/10^2}{1-2/10+1/10^3}\)=3.6829

Answer 24

try it for n=100: we get 3.060711

Answer 25

try it for n=1000: we get 3.00600701102

Answer 26

try for n=10000: we get 3.00060007

Answer 27

The higher to infinity we go it gets closer to 3. So as n approaches infinity we get 3

Answer 28

yes... now, let's see why

Answer 29

as n becomes larger and larger, the terms with n^2 and n in the denominator become closer and closer to zero

Answer 30

as n approaches infinity, these terms approach zero

Answer 31

and we are simply left with 3/1=3

Answer 32

That makes so much sense now! Thank you so much.

Answer 33

np... just remember the rules you were taught in class: you have to divide by the term of the largest degree to be able to approach the problem like I did