3 ms·
I notice that I stumble over math over small but important details. I understand the big ideas, but then at chapter 4 in the book it says: y+dy = (x+dx)^-2 is
by mettamage 8y ago
I notice that I stumble over math over small but important details. I understand the big ideas, but then at chapter 4 in the book it says:
y+dy = (x+dx)^-2
is equal to
x^−2 * (1 + dx/x)^−2
[1]
To me (not that strong at math) this isn't apparent at all.
I have a couple of options here:
1. Spend a couple of hours fiddling around and trying to figure out the answer.
2. Hopefully find some app.
3. Ask a friend.
Regarding the options: I don't have a friend and I don't have an app. If you wouldn't know how to solve this, then what other strategies for understanding this are there?
[1] The LaTeX version:
y+dy &= (x+dx)^{-2} \\
&= x^{-2} \left(1 + \frac{dx}{x}\right)^{-2}
- gspetr 8y ago4. Try to look for a different (one you might understand better) explanation of the same concept in different sources. These can be youtube videos, other books, math.stackexchange.com, math forums, etc.
- mettamage 8y agoHaha I'm now looking at Khan Academy. I went to https://tutorme.com/ https://tutorme.com/ and went on a free trial.
- fesoliveira 8y agoFrom your other post, you might have been a bit tired due to sleep deprivation, so don't be too hard on yourself for not getting it ;) As for the expression, you just have to expand it: y+dy = (x+dx)^-2 = 1 / (x+dx)^2 = 1 / (x^2 + 2xdx + d^2x) = 1 / [x^2 * (1 + 2dx/x + d^2x / x^2)] = 1 / [x^2 * (1 + dx/x)^2] = [x^2 * (1 + dx/x)^2]^-1 = x^-2 * (1 + dx/x)^-2 It looks like a bit of a jump at first, but he just skipped the expansion of the expression. When I see this kind of thing, it helps me to just mess around with both start and end to see if I can find a way to get from one to the other.