>>13181603what am I regurgitating?
the original sequence is clearly incrementing natural number of x^2, which I even stated.
and their different, delta is a sequence and the different of that is 2.
d/dx x^2 = 2x
I didn't regurgitate anything, I explained the meaning. That's the difference, you're implicating that it's all meaning less numbers and equations but it's very much the opposite.
there is intuition always all the time.
this
>>13180707 look like something familiar? looks suspiciously like the definition of linear slope, the rate of the change of y over that of x.
y = mx + b, an extremely simple function.
x in R maps to y by the definition that x is m many more x plus b.
if you were to put a line through a function, say x^2, it may go through two points, and if you were to alter that secant line so that the second point that determines it approaches the first then it approaches a tangent line on P1. The slope of that tangent line is then defined as the instantaneous slope of that function at that point.
generalize this for any any for any function
>>13180707how can you not see how meaningful that is? I literally spoon-fed you the meaning.
if we saw a line we'd describe it in english, math then formalizes that image and description.
math is beautiful.
