00:01
We want to find the equation of the tangent line on the curve y is equal to square root of x at the point 1 -1.
00:08
Now, recall to find the slope of the tangent line.
00:12
This is going to be the limit as x approaches 1, so it's our x value that we want to get really close to, of f of x, minus, minus, all over x minus 1.
00:27
So this is how we would set it up.
00:31
And now let's just go ahead and plug everything in.
00:35
So this is going to be the limit as x approaches 1 of the square root of x minus 1 over x minus 1 because remember f of 1 is really just this value right here.
00:52
So now in this case, what we can do, because if we just plug this in directly, we'd get 0 over 0, which i don't know what that means.
01:05
But we can factor the denominator in the following way to give us the square root of x minus 1 times the square root of x plus 1 all over the square root of x minus 1.
01:24
And now notice those cancel out with each other...