00:01
For this problem, we want to estimate the limit of sine of 4x over x as x approach as 0.
00:06
So the first thing we have to do is to set f of x equal to sine of 4x over x, and then we make a table of values, or x values close to 0 from the left or from the right, and then from there we determine the value of our f of x here.
00:27
And then once we have the values, we analyze where this value approach to as we get closer to zero either from the left or from the right.
00:39
So let's consider this table below.
00:43
For the first column, we choose x values left of 0.
00:48
So let's say negative 0 .002, negative 0 .001, negative 0 .05, and then negative 0 .05.
00:58
0 .001.
01:01
For the third column, you choose x values right of 0 .0 .0 .02, 0 .001, 0 .0 .05, and then 0 .001.
01:17
When x is 0 .002, the negative 1.
01:22
The value of the function is 3 .99999.
01:32
57333.
01:34
When it's negative 0 .001, the value of the function is 3 .9999 -89333...