Mathematics

Problem

For

x\le \dfrac{\pi}{2}

, let

\dfrac{dy}{dx}=y+\sin x

and suppose

y\bigl(\tfrac{\pi}{4}\bigr)=1

. Take one tangent-line step of size

h=0.30

starting at

x=\tfrac{\pi}{4}

. If the slope used in the calculation is first rounded to three decimal places, which of the following is the resulting approximation of

y\bigl(\tfrac{\pi}{4}+0.30\bigr)

to the nearest thousandth? a)

1.565

1.212

1.512

1.536