For , let and suppose . Take one tangent-line step of size starting at . If the slope…

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

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

(b)

1.212

(c)

1.512

(d)

1.536