Question

Which of the following is the best linear approximation for f(x) = cos(x) near x = pi/2 ?

Answer 1

we can approximate y(x) with L(x)
y(x) ~ L(x) ,
where
L(x) = y (a) + y ' (a) ( x - a)

Answer 2

where the approximation is very good as x -> a

Answer 3

L(x) = cos(pi/2) + (-sin (pi/2)) * (x - pi/2)

Answer 4

which is L(x) = 0 + (- 1) * (x - pi/2)

Answer 5

-x + pi/2

Answer 6

yes that looks correct