@viktorlogos@DarkCyan12@ChauDocTourist@Rainmaker1973 Total mass 100kg. 99% (99kg) is water so 1% (1kg) is dry. 1kg dry remains constant when water is removed. Remove water until 98% water, here 2% is dry (Still 1kg dry). Now, if 2% is 1kg then 100% is 50kg.
@geomathsblog The critical step is 8×10=80 exactly. If you don't have a = sign showing that, you don't have a complete logical argument (that is you don't have correct "working out").
@geomathsblog The first is correct. Even if written on two lines, still use an = sign. Maths is read from left to right, line by line and a new line can be introduced anywhere. We do not read top left diagonally to bottom right.
@DavidKButlerUoA Ah, I think I misunderstood. Are you asking: If f'(c) exists and equals 0 for some f, and if is convex on an open interval bounded by above by c and convex on an open interval bounded below by c, is f necessary convex on a neighbourhood of c?
@blatherwick_sam@mrsouthernmaths A way of describing how functions behave as 𝑛 → ∞, useful for comparing whether one functions dominates another, describing asymptotic behaviour, or in computer science whether one algorithm is computationally more efficient than another.
@blatherwick_sam@mrsouthernmaths Yes, using Big O notation, a linear function is O(n) and a cubic is O(n^3). Every O(n^3) function will eventually overtake any O(n) function.
@JoelBSperanza@DavidKButlerUoA Are you doing boundary value problems and initial value problems? I found when I studied engineering these were some of the most exciting types of problems.