Integration and dx [closed] - math

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I'm writing a calculator for iOS and need to know a very basic thing: is an integral w.r.t x appended with a dx or a δx and why? I understand δ is an infinitesimally small value whereas a dx is a very small value but which is correct?

dx is the correct notation. Wiki on integral

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Difference between ∑ and ∑1 [closed]

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I learn a deterministic final automat, nondeterministic,regex... And I found that is important to know a difference between ∑ and ∑1 since they both the same if ∑={0,1}, but I will answer that ∑1 is result of concatenation epsilon and 0,and the epsilon and 1.How would you answer that the question is asked by the professor?
Well, sigma is a finite set of input symbols called the alphabet ∑.
∑1 on the other hand is the word w consisting of one letter of the alphabet ∑, hence the 1 in ∑.

How do we get the remainder in division arithmetic for computer architecture? [closed]

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I am learning binary division following the step-by-step procedure. I am stuck at Step One Repeat One in the remainder section. To get the remainder, the formula is Remainder = Remainder - Divisor.
How do we get to remainder: 11100110? I just don't understand how we have 1110 on the left half of the register. Any guides or help would greatly be appreciated!
Thanks:
The example is 10/5 using an 8 bit ALU.
I have attached a picture of the example for reference

How to calculate "Sn = 1*1+2*2+3*3+...+n*n " (N>=1) [closed]

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How to calculate this series Sn=1*1+2*2+3*3+...+n*n where (n>1).
Please give me hint
From this page, the following formula can be used
Please post math questions on http://math.stackexchange.com. SO is for programming-related questions.
According to Wikipedia
S = n * (n + 1) * (2*n + 1) / 6
It is easy to prove this using induction.

I have a math problem and I love stackoverflow [closed]

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I know it's not programming question but I thought we could all use the challenge :)
Link to diagram
Point A is the source of a laser. It is shinned at a single mirror and then reflected to another mirror finally arriving at point B ... see picture.
The goal is to find the total distance of all the lines.
I am not a student and this is not homework.
Same as a straight line from (-x, y) to (a, -b).
sqrt((a+x)^2 + (b+y)^2)

Algorithm to determine the minimal set of coins you should carry to always make exact change [closed]

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US coin values:
.01, .05, .10, .25
What is an algorithm to determine what configuration(s) of US coins can be used to match every value from .01-.99 using the fewest coins possible?

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