00:01
Okay, so we want to find our equation of our tangent line, given our x value.
00:06
This time our x value is equal to 9.
00:08
So this a term is 9.
00:10
So we're going to need to find our slope and a point on our line.
00:14
Well, we're given our x terms, so let's find our corresponding y term.
00:17
So let's label this x1, and then y1, that's going to be equal to f of a, which is equal to f of our x1, so that's 9.
00:27
So that's equal to 4 times the square root of 9.
00:32
So that's 4 times 3, which is equal to 12.
00:35
So now let's also find our slope.
00:40
So that's f prime of 9.
00:43
Well, actually, let's write out our points, x1, comma, y1.
00:47
That's equal to 9 .12.
00:50
Okay, so our slope, that's equal to the limits as x approaches a, which is 9.
00:55
Of f of x, that's four square roots of x minus f of a, which is 12, and that's all over x minus nine.
01:06
So in our numerator, we see that we have a four in common, so let's factor that out.
01:11
So we have four, and then the square root of x minus three over x minus nine.
01:16
And now if we use the x -sub, we have division by zero.
01:19
So instead, let's multiply and divide by a conjugate to solve for our limit...