Mathematics

Problem

Suppose

\displaystyle \frac{dy}{dx}=y\cos x

with

y\!\left(\tfrac{\pi}{2}\right)=1

. A student begins at

x=\tfrac{\pi}{2}

and advances in equal increments of

\Delta x=\tfrac{\pi}{6}

, updating

y

at each step. After three such increments, what is the student’s approximation to

y(\pi)

? a)

0.545

0.404

0.738

0.609