Question

Are there any other ways than graphing to find the limit of a function?

Answer 1

I believe that substituting the variable to the value it is approaching to is a way to simplify the limit, but is there anything else that allows me to compute a limit directly?

Answer 2

You can use a graphing calculator to get the exact decimal up to the limit and then write it down. I dont know how to find that without a graphing calculator

Answer 3

Yep—I do use a graphing calculator. Is there any manual way?

Answer 4

summation of an infinite series has a few tricks

Answer 5

Sure.. I'd love to know 'em.

Answer 6

if the sequence of partial sums has a formula, you can take the limit of the partial sums

Answer 7

Well, you can always use epsilon-delta to find limits if you really want to :)

Answer 8

Uh-oh. Not that definition again :P

Answer 9

Haha you dont really want to go that route. I have a challenge solve the reimann hypothesis. You will get 2 million.

Answer 10

i never did get used to the definition part; the concept is simple enough tho

Answer 11

May I have an algebraic example, Amistre?

Answer 12

Yep. The concept is good enough, but a mortal can't find the limit of a function without using technical help :P

Answer 13

oh, so this is with algebra and rational functions?

Answer 14

The concept only seems simple if you don't get used to the definition :P Limits, imho, are the most fundamental and important concept in calculus, which is why the definition is a hassle :P

Answer 15

I mean—may I have an example to make that explanation easier?

Answer 16

i cant think of one at the moment :/ too much chicken nuggets for lunch

Answer 17

I wouldn't worry too much about infinite series quite yet, Parth. For the things you're learning I think you'll be okay with graphing and with plugging in values near the value that you want.

Answer 18

Depends on the limit. Remember the link and other advice i gave someone yesterday (i believe you commented on the question) about limits going to infinity?

Answer 19

Snacks always mess up your mind. I see what you mean, Amistre :)

Answer 20

It is fine to just use your intuition with limits, once you have that intuition developed. So, for example, let's look at the function f(x)=1/x as x approaches infinity. If we want to find that limit, there are a few ways. We can look at the graph, and we see that the graph looks like it approaches zero. Or, we can think about what happens as we plug in larger and larger values of x. You can see that the result gets smaller and smaller and smaller, but will never actually reach zero, but, the limit is zero.

Answer 21

Yeah. I try plugging in values as suggested by the first reply.

Answer 22

I think the best way is to play around with a lot of limits so that you get a good intuition for them.

Answer 23

Thank you! I do need a lot more practice as this is only a start :)

Answer 24

Also, to suck up, I have no idea of your Mathematical level; as I go bigger and bigger, I'd begin to realise where you actually are ;)

I'd be testing your Calculus skills in the days coming over, Nathan. :P

Answer 25

My calculus skills need some testing, so I'm all for it :) But, I am going on vacation tomorrow for almost two weeks, so I'm not sure how much I'll be here.

Answer 26

No worries! I may wait for 2 weeks heh.

Answer 27

No way, I want to come back and have you be doing integrals already! :P

Answer 28

The worst thing is that you'd miss out my birthday. Hmm.

Answer 29

Lol!

Answer 30

Limits approaching anything other than 0 or infinity will always result in a numerical answer or DNE(does not exist)
Limits approaching infinity can be evaluated by noticing the ratio's of the largest polynomials. If it's not a polynomial, IE: e^(-x), or something else, then you have to understand the graph of that function and what happens as it approaches infinity? (asymptotes??)
Limits approaching 0 are kind of like limits approaching infinity but "backwards" IE:\[{1 \over 0} = \infty\]\[{1 \over \infty}=0\] keep that in mind when evaluating limits. usually limits going to zero involve some polynomial and you just have to figure out how to factor it correctly so that the denominator doesn't go to zero.

Answer 31

Haha! That was a nice one!