help math

[sky]

a) f(x)= 2x -1
b) ( f(a+h) - f(a) ) / h
--> compare your result in part b to the equation for f(x). what can you conclude ?
i solved this problem already, but i don't know how to explain this question in english. my english is kind of poor.
:(
please help me

[NguyenKhang]

So [f(a+h) - f(a)]/h = 2

The conclusion is based on the math level...
- One can be: It is a slope of f(x)
- The other one can be something related to limitation, which NK don't remember exactly.

Hope this help.
NK

[Trung Quốc]

Write down the whole things, so that we can understand it and explain it better. :)

b) the definition of limit, in which
lim (h-->0) of ((f(a+h)-f(a))/h) will equal to f(a) :)

QT

[Chris-T]

From eq(a) : f(x)= 2x -1 ==> This is eq. of a straight line, which has
slope m=2.

From (b): Find ( f(a+h) - f(a) ) / h, which I believe answer is "2" also,
just as NK said. Intuitively thinking for easier remembering &
understanding. Look at eq(b), there is "numerator" and "denominator".
The "denominator" can be viewed as a "change" in x, (in this case = h).
And the top/numerator can be viewed as the "corresponding change"
in y or f(x) if x change an amount of "h". Then one can say that eq(b)
calculate the "change in y" over (or divided by) the "change in x"; or
similarly it's considerred as "Rise over Run", which is mathematically
referred (or called) as the "slope" of the straight line. The explanation
is long for your understanding, but the answer is short as NK's, "It's
the slope of the line represented by f(x)=2x-1, and this slope is m=2".:morelove:

From your question, I think that you have not reached to section/
chapter about the "limit" yet (coming soon). For your preparation, the
"limit" theorem will be similar as QT's explanation (except that it will
equal to f'(a) not f(a), probably QT's typo only). Ultimately, the limit
theorem will lead you to find the "slope" of any curve (not just the
straight line as this example) at any given point on the curve. Most
people would find the "limit" is very "abstract" and difficult - so be
prepared. It's the mathematic theory to lead to other much more
convinience ways of manipulate many other theories/concepts later.
Try to get the "basic" & fundamental straight with depth/solid
understanding now, and it would help you more in the long run
(if you're pursuing futher in this area). Just a personal suggestion.

[sky]

thanks you guys
it was very helpful !!!!!