00:01
Okay, so let's sketch this vector field f given by y, comma, 2x.
00:09
We are going to sketch this guy in the cartesian plan, x, y.
00:15
And well, how are we going to do this? we are going to use five points, the origin, the point, one, one, the point negative one, one, the point negative 1 negative 1 this one and finally the point 1 negative 1 okay perfect so let's do it well the value of f at the origin here is just 0 so nothing the value at 1 1 is the vector 1 comma 2 so it's gonna be like this this is the vector v equals 1 comma 2 then for the point 1 negative 1 we are gonna have what well we are gonna have the vector v equals okay negative 1 comma 2 so it's gonna be like this perfect so this is negative 1 comma 2 then at the point negative 1, 1.
01:31
Here, what are we going to have? well, we are going to have 1 negative 2.
01:37
So 1, negative 2, which is going to look like this one here.
01:44
Okay, basically the same as this one, but in the opposite direction.
01:50
Finally, for the point, negative 1, negative 1, we are going to have negative 1, negative 2.
01:57
So we are going to have a vector like this...