00:01
To find the equation of a tangent line, we first need to know the slope of that tangent line.
00:06
And to do so, we'll use our friend the limit definition, which i've circled in this box.
00:12
So that definition is essentially the limit of a sequence slope.
00:16
It's the limit as h approaches zero, h being the run of the change in y over the change in x.
00:23
And remember, c is the x value that we're interested in, which would be zero in this case.
00:28
So let's find that tangent slope.
00:33
We need the limit as h approaches zero of our function.
00:36
Note this is f of x, if you will, evaluated at c plus h.
00:42
Well, c is zero and zero plus h is h.
00:46
So if we plug h into our function, we get that.
00:50
Now we need to subtract our function evaluated at c.
00:53
C being zero would mean plug zero into our function.
00:57
We get 1 over 0 minus 1.
01:00
And all of that divided by h.
01:05
So essentially we have 1 over h minus 1 plus 1 all over h.
01:13
Let's get a common denominator.
01:16
We can write 1 as h minus 1 over h minus 1.
01:22
So the two fractions in the numerator can combine...