>>11955857>convergence of functions, even uniform, doesn't imply convergence of derivativesThat's right. Therefore you CAN'T assume that a series such as:
.9
.99
.999
.9999
.99999
...will have 1 as its conclusion. There simply is no "conclusion" to this, just like there is no "last nine" at the end of .999...
Pictured: Line BW has a slope of 0. Line BZ has an infinitesimal slope. They are clearly different lines that arrive at different points, and only intersect at 0,0.
