00:01
In this problem, we're given a function f of xy, which is equal to the sine of x times the tangent of y.
00:07
And we want to compute the linear approximation here.
00:10
So we can do that for each function.
00:12
We can write that the sign of x is going to be equal to the sign of zero plus x times the derivative of sine of x evaluated at x equals zero and then higher order terms.
00:25
And here, this is equal to the cosine of x.
00:28
And when cosine of x is at zero, it's just equal to 1.
00:31
So this is approximately equal to x.
00:34
We can do the same thing with the tangent of y.
00:36
This is going to be equal to the tangent of 0 plus y times the derivative of tangent y.
00:44
I see i have an x here instead of a y, so i'll fix that.
00:49
Evaluated at y equal 0.
00:51
This is equal to the secant squared of y.
00:55
Remember this is 1 over the cosine of y.
00:58
And when y is equal to zero, this is actually equal to one.
01:01
The sequence squared of zero is equal to one.
01:04
And so this is also equal to zero.
01:07
And so again, we just have y...