Limits

[The_Dude]

I'm lost at how to do this problem.




Any help would be appreciated.

[GreasyP]

I stared at it for a full minute before I realized it wasn't a 5-part problem, it's multiple choice. The answer is #1. Just plug f(x) into that first equation (which is just the definition of the derivative) and you'll get a answer yourself easy enough.

[BuddyHawks]

Once you learn the Chain Rule, you will be pissed that your professor didn't teach you it the first day of class. It makes solving those problems possible in seconds.

[TIO]

Have you done differentiation yet? That limit is just first-principles differetiation of f(x). Works for any (differentiable) f(x).

[sieger35]

Hey, let's see if I can remember how to do it, the answer that was previously mentioned (#1) is correct, and it can easily be solved by the chain rule[which is second nature, once you learn it]. However, what you are given here is the formal definition of a limit. To see how to get the answer of 6x+4 here are the complete mathematical steps:

Ok the first part says f(x+h), so that means take your f(x) equation and h to every x term you see:

3(x+h)^2 + 4(x+h) + 2


and that's basically it, now apply the equation

lim as h->0 f(x+h) - f(x) / h

so... we have:

lim h->0 (3(x+h)^2 + 4(x+h) + 2 - [3x^2 + 4x + 2]) / h

lim h->0 (3x^2 + 6xh + 3h^2 + 4x + 4h + 2 - [3x^2 + 4x + 2]) / h

now, perform some cancellations and you have:

lim h->0 (6xh + 3h^2 + 4h) / h now.. you see a common factor of h, which can also be cancelled, so you're left with:

lim h->0 (6x+3h+4)
ok, you may be saying what!?! that's not the answer.. now, you simply plug in 0 for h, so you have as a final answer: f`=dy/dx = 6x + 4

Hope this clarifies your problem and closes the book on this thread :-)

P.S. Make sure you continuously write lim h->0 for each step as I did, teachers are notorious for taking points off for not including that, since it is a formal definition of a limit.

[TIO]

Originally posted by sieger35
However, what you are given here is the formal definition of a limit.

No, that's the formal (or, more accurately, the first principles) definition of a derivative.

[sieger35]

Yes, you are correct, I made the wrong statement (hehe, sorry it was almost 4 am when I posted :-) ). However, I made the right notation of f`=dy/dx= 6x+4

[inkriminator]

man, does this bring back memories. bad bad, horrible memories...

[stldickie]

that made me tired, now im reliving my deficient past

[MacGnG]

http://mathworld.wolfram.com/Derivative.html

THIS IS THE SHORT WAY (sorta)
3x^2 + 4x + 2
ax^n + bx + c --- a,b,c, are constants

(n*a)X^(n-1) +b --- c is a constant so it becomes 0
(3*2)X^(2-1) +4

=6X + 4

[quantumburnz]

I love calculus

Ahh.. shortcuts are the world. Beautiful Integrating Factors.. Blah Blah Blah...

[Sapper]

Some very good answers here.

Change f(x)= 3x^2 + 4x + 2 into "box"

Then plug "box" into the differentiation formula in place of "x".

you get: (box - h) - box / h

now simplify the terms using the real value of "x" (ie. 3x^2 + 4x + 2)

Later on, you will learn "the power rule" which simply states:

where f(x)= x ^ 3
f ' (x)= [exp] x ^ [exp - 1]

ie. f ' (x) = 3x^2

.. much better

In your case:

f(x)=3x^2 + 4x + 2

f ' (x)=6x + 4x + 0

PS: you will notice that the derivitave of any "real number" is always 0

[Dilbert1234567]

oh god i hate calc

[Sapper]

Lol. It's not that bad ... really ...

Honestly, I used to fear math .. until I decided - fuck it! I will work my ass off and actually master the topic. Incidently, I no longer have an ass .. but I do understand calculus.

[TIO]

uh...how much of it, Sapper? Multivariate? Manifolds? If so, there's a senior lecturer around here who would love for you to explain it to him!

There's a lot more to Calc than derivatives and the kind of integrals you encounter in grade school!

[Sapper]

TIO, a tad anal or what? Wow.

You obviously can not appreciate the notion of understanding something. Not that it really matters - what you think is of no consequence to me.

PS: Because you seem to lack fundamental social skills, I will take this to mean that you also lack fundemental logic skills. You should take special note that I said: "I will work my ass off and actually master the topic" and not "I will work my ass off and actually have mastered the topic".

[yournamehere]

Heh heh - wait till 3 semesters from now, when your Differential Equations professor informs you that up until now, you've been doing it all backwards.

[Sapper]

Lol. That'll be a great day