Using the linear approximation to f(x) = cos x at the point x = 1 to estimate
the value of cos(1.03) works well because cos x looks like a line when you zoom
in on it.
true/false
I say it's false since you don't know an exact value for cos(1), and since there is a closer exact value near 1.03, such as .
I may have answered this in a different way than the question expects you to answer.
The linear approximation takes on the form
So, is a good approximation to ?
Now,
This is a pretty good approximation, with an error of about .
If you were to zoom in on the cosine function at about 1, it appears linear:
Here's a graph of the function with its linear approximation:
(the blue line is and the purple is
So I would say its true.
--Chris