Question

Find the limit of a position function?

Answer 1

what function ?

Answer 2

@amoodarya -- check the file that I attached.

Answer 3

if you're interested in newtonian mechanic you should learn some things first. ex. v=dS/dt where S is the distance. Basically you're looking for the derivative of the distance. It'd be much simpler for you if you check out what a derivative is and read on some newton mechanics. It's really fun.

Answer 4

i hope she knows derivative

Answer 5

@amoodarya -- I actually haven't learned derivatives, yet. Ironically, this the sections of my textbook prior to derivatives...

Answer 6

understand ?

Answer 7

That is the definition of the derivative. and is like using (f o g).
But instead, you are plugging in, "a" for t. And taking the limit of the whole function. These types of problems are very heavy in algebra so I suggest that you really show every step of ur work to not get lost.

Answer 8

Shouldn't the answer be 16a? x: Not sure if it was a mistake or not.

Answer 9

I believe it should be -32a.

Answer 10

yes the derivative of ax^n is a*n*x^n-1, so it's -32a

Answer 11

Yeah, I have no idea where this -32 comes from.

Answer 12

well i explained above -16x^2 you take the 2 put it in front and substract one from the degree
so you get -16*2*x^(2-1)=-32*x

Answer 13

that is a formula for the derivative of a polynomial and not an easy one to prove for real numbers

Answer 14

@mivanov that's correct, but they have not learned derivatives yet and must first learn the definition prior to doing derivavites.

Answer 15

ok, then just calculate it as a normal limes, doing it for a second degree is easy. the hard thing is prooving that dx^n/dx=nx^n-1, but they don't ask for it, they just want her to find a simple limes of polynomial of degree 2

Answer 16

I believe @amoodarya did it earlier. Like I said, these problems are algebraically tedious. It's all that you are doing here. Not much calculus, aside from limits.

Answer 17

All right. Well, let me try to work this out and see what I come up with. Thank you for all that input, everyone. It wil does help.

Answer 18

well, i wish you luck :)
real analysis is a fun thing, do not let these easy limits get you down.

Answer 19

Thanks, it's frustrating
that "easy" problems give me such a hard time.

Answer 20

well easy is a different thing for different persons, if you get deeper into analysis, you will see that you have to learn set theory, relations, partial orders, functions, natural, rational,real and complex numbers, then groups, ring,fields, polynomials as well ,and vector spaces, and only after that i think one is ready to talk about limits and derivatives.
so in my opinion even through i can solve most real analysis problems i am not worthy because i haven't learned all that stuff i mentioned good enough :D. But in school they won't bother you with all of these so don't get scared. :)

Answer 21

-32a is answer
if i had mistake in what i write because i draw it

Answer 22

Well, I'm pretty much teaching myself all this math -- online college classes/ Our teachers are just available for questions, but they don't teach the material to us. :/

Answer 23

well i would advise if you like this stuff, to find a book about real analysis. it encompasses - limits,derivatives,integrals and more :) still don't bother if you don't like it. people shouldn't do what they dislike.