Why dose 2 = 1?

Question

In my calculous class this equation was presented to the calss:
x*x = x + x + x + ... + x (x times)
d/dx (x*x) = d/dx ( x + x + x + ... + x )
d/dx (x*x) = d/dx (x) + d/dx (x) + ... d/dx (x)
2x = 1 + 1 + ... + 1
2x = x
2 = 1

I do not understand why this works. If possible coul you pleasse explain why it works. In addition to why it techiquenly does not.

Answer 1

It doesn't work. The problem is in the expression x+x+...+x (x times).
Since x is a variable, we cannot say x times, since a small change in x affects the number of times it appears.

Think about the definition of the derivative. A small change in x (of h) in this case also changes the number of terms.
So we have x+h + x+h + .... (x+h) times, NOT x times.

Answer 2

It works or rather it does not work because d/dx ( x + x + x + ... + x ) does NOT equal d/dx (x) + d/dx (x) + ... d/dx (x) . You cannot distribute derivative over the sum of a variable number of summands (such as x summands).

And, of course, you abuse the difference between reals and integers. The first line only makes sense if x is an integer, the rest -- only if x is real.

Answer 3

Well, there is an assumption here that x is a discrete variable like 1, 2, 3, and not a real variable.

Otherwise, you cannot make the assumption that:

x*x = x many x's as this is only true for integers. Calculus does not work on integer valued fuctions.

Answer 4

you are able to desire to easily take drugs as they are prescribe to you thru your known practitioner. yet to respond to the question. in case you're taking 2 pills on a similar time and the prescription says to take one, it is an overdose yet COUNTS and one dose.

Answer 5

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Answer 6

There is something wrong with your equation.
Why is 1+1...+1 equal to x
Not to sure what you were trying to prove. I need more information, is it series or sequence. It looks more like Statistics than Calculus...

Answer 7

not only do you need help with mathematics but you need a tutor to bring you up to standard in English

Sorry but it is very frustrating trying to translate questions and believe me you are not alone. I do not mean to be mean but you will get better answers if you use correct spelling and grammar

Answer 8

because all the x's are of the same value. So, x is actually 2/2.

Answer 9

Thats because X is a variable dear..and 2x=x doesnt make sense..

Answer 10

I don't know calculus, but assuming your answer is correct then the equation must be false.