Limits
 

I'm lost at how to do this problem.


http://www.cox-internet.com/ashish/help.jpg

Any help would be appreciated.

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.

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.

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

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.

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

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

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

that made me tired, now im reliving my deficient past

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

I love calculus :)

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

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 :D

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

oh god i hate calc

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

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.

:p

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!

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".

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.

Lol. That'll be a great day :) :p