A classic example to learn the concept limit in math is the race between the xoxelho (a cute rabbit) and the turtle. Imagine a race track, the turtle is 1 meter from the victory and the xoxelho is 10 meters from the victory. The turtle runs at 1 m / s and the xoxelho at 10 m / s. It is not difficult to see that the two will arrive in victory at the same time. Because in 1 second the turtle moves the 1 meter left and the xoxelho moves the 10 meters left.
However, except for the arrival position, in this race the xoxelho will never overtake the turtle. To better understand this, we will make some calculations of your positions by the time.
0.1 seconds: xoxelho at 1.0 m, turtle at 9.1 m
0.2 seconds: xoxelho at 2.0 m, turtle at 9.2 m
…
0.9 seconds: xoxelho at 9.0 m, turtle at 9.9 m
0.91 seconds: xoxelho at 9.10 m, turtle at 9, 91 m
0.92 seconds: xoxelho at 9.20 m, turtle at 9, 92 m
…
0.99 seconds: xoxelho at 9.90 m, turtle at 9, 99 m
0.991 seconds: xoxelho at 9.910 m, turtle at 9, 991 m
0.992 seconds: xoxelho at 9,920 m, turtle at 9, 992 m
…
0.999 seconds: xoxelho at 9,990 m, turtle at 9, 9999 m
Thus, although the xoxelho is faster than the turtle, during the whole race, the xoxelho was always behind her, except for the occasion of victory, where they both drew.
With this, if the “1st place” function is given by the animal that is in front in a determined time of this race, we have that in the limit with the variable time tending to 1 (that is, the time as close to 1 as we want), this limit will be equal to the turtle. That is, for any time (although very close to 1), the turtle will always occupy the 1st place in this race.
Below I synthesize these same ideas in a short video.
Xoxelho 