00:01
Okay, so we want to find the slope of our tangent line given our x value.
00:05
So here we have that our x is equal to 2.
00:07
So that's our a value.
00:09
So let's replace our a with 2.
00:11
Okay, so let's use this equation here to find our slope.
00:14
So here we have f of x, and we also need to find f of a.
00:18
Well, we said that a was 2.
00:21
So we get 1 over 2 plus 1, which is equal to 3 over 2.
00:25
And now let's also find x minus a, that's equal to x minus 2.
00:30
Okay, now let's plug this information.
00:32
Into our following equation here.
00:34
So we have the limit as x approaches to of f of x, that's 1 over x plus 1 minus 3 over 2, all over x minus 2.
00:46
Okay, so let's simplify our numerator...