# What is the lim q>p of [f(p+q)-f(p)]/q?

1. Dec 17, 2013

### TitoSmooth

I did. [f(p)+f(q)-f(p)]/q = f(q)/q

Can anyone explain what the f outside of parenthesis mean? Is it function of letter? and whats the answer.

Thanks.

2. Dec 17, 2013

### Decimae

Why do you say $f(p + q) = f(p) + f(q)$. Do you know what $f$ means? If so, you haven't given that the function $f$ is linear, so you can't do that.

If you don't know what $f$ means, it means it is a function(probably, based on what you need to calculate). A function is a way to notate something done on a number, for instance take the function $g$ which we define to be $g(x) = x^2$ for all real numbers $x$. Then $g(2) = 4$, for instance. That also means that $g(p + q) = (p + q)^2 = p^2 + 2pq + q^2 \neq p^2 + q^2 = g(p) + g(q)$.

3. Dec 17, 2013

### TitoSmooth

sorry.

it is basicly problem 7. pg 104 in Morris Kline Calculus.

what is Lim q→0 [f(p+q)-f(p)]/q.

what does this mean? the f(terms) are confusing me.

Im in the section where we learn X^n rule of derivatives.

4. Dec 17, 2013

### LCKurtz

Are you given a particular function $f$ to begin with? Or is it just some unknown function? If you think of $q=h$ and $p=x$ you have$$\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$$Is that familiar?

5. Dec 17, 2013

### TitoSmooth

Nope not familiar and it does not say its a function or not.

6. Dec 17, 2013

### dirk_mec1

Is q>p or is q ->p?

7. Dec 17, 2013

### TitoSmooth

q---> as q nears p

8. Dec 17, 2013

### vela

Staff Emeritus
What specifically is confusing you? It was explained above that f denotes a function.

9. Dec 17, 2013

### TitoSmooth

Can I have a step by step explanation of the question I posted? How do I find the limit of the problem.

10. Dec 22, 2013

### Staff: Mentor

You're fairly new here, so might not be clear on how things work at PF. Per the rules of this forum, we don't do your work for you.

In the rules, under Homework Help Guidelines:
It seems pretty obvious to me that the expressions f(p + q) and f(p) are function notation, and the limit suggests a difference quotient, a basic concept in calculus. It would actually be a difference quotient if it were like this:
$$\lim_{q \to 0}\frac{f(p + q) - f(p)}{q}$$
This isn't what you wrote, though, as you have q approaching p rather than 0.

A more serious problem is that you converted f(p + q) to f(p) + f(q), which is almost never a valid step. As you said earlier, you didn't understand what the notation f(p) meant, which tells me that you will have a very difficult time in calculus until you fill this gap in your knowledge.

11. Dec 22, 2013

### SammyS

Staff Emeritus
What Mark44 wrote is exactly the problem you referred to.

What is $\displaystyle \lim_{q \to 0}\frac{f(p + q) - f(p)}{q}\ \ ?$

12. Dec 22, 2013

### Staff: Mentor

From the thread title, the limit was as q --> p, which doesn't make much sense. I didn't notice that in post #3, the OP changed it to q --> 0.

13. Dec 22, 2013

### SammyS

Staff Emeritus
Yes, the limit is as q --> 0 .