Weird First Principles
- Thread starter StaticX
- Start date
I know that this is going to sound flip, but in fact you are given a step-by step recipe in the formula for the Newton quotient.Basically got some homework and im stuck on d) e) and f)
My teacher wants us to use the f(x+h) - f(x) / h formula and i literally have no clue on how to do these help please
Let's take problem (a)
\(\displaystyle f(x) = 3x^2 + 4x + 3 \implies f(x + h) = what?\) Work it out fully.
So \(\displaystyle f(x + h) - f(x) =what?\) Straight forward so far, right. Just simple algebra.
So \(\displaystyle \dfrac{f(x + h) - f(x)}{h} = what?\)
Up to this point, you have done nothing but very basic algebra, and the formula tells you what algebra to do. Tell us what you get to here, and tell us if you can finish or not from that point.
No I said at the start of the post I'm only stuck on D) E) and F) i get to f(x+h) i don't know if it should be 3/x + h or 3/x+h
like this =>
Like I can do the basic algebra but for the first one which is Question D I'm not sure if it's right
:idea: I know what you intend, but putting spaces around the plus sign doesn't change the order of operations. Without grouping symbols, those two expressions are the same.
f(n) = 3/n
Let n = x + h
f(x + h) = 3/(x + h)
Does the intermediary step above help clear up your uncertainty?
Please show your work, if you get stuck on the rest of it.
Cheers :cool:
Last edited:
this is what I got i think it may be right but how do i get past this thanks for the replies
http://ft2.fckitupload.com/XIbf/IMG_0543.JPG
D
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Now you have:
\(\displaystyle \dfrac{f(x+h)-f(x)}{h} \ = \ -\dfrac{3h}{x(x+h)} \ * \ \dfrac{1}{h}\)
\(\displaystyle \dfrac{f(x+h)-f(x)}{h} \ = \ -\dfrac{3}{x(x+h)} \ \)
now take the limit h→0.