A student wishes to sketch a slope field for the differential equation over the…

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A student wishes to sketch a slope field for the differential equation

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

over the rectangle

0\le x\le 2\pi

-3\le y\le 3

. Because the right-hand side depends only on

x

, the student realizes that evaluating

\dfrac{dy}{dx}

at a smaller subset of lattice points is sufficient to determine all segment directions. Which of the following subsets is the smallest that still provides enough information to complete the entire slope field in the given rectangle? (a) All lattice points where

y=0

and

x

is a multiple of

\pi

within

0\le x\le 2\pi

(b) All lattice points where

y=0

and

x

is a multiple of

\pi/6

within

0\le x\le 2\pi

x=0

and

y

is an integer between

-3

and

3

(d) All lattice points where

x

and

y

are both integers in the rectangle

Related theory

Visualization
Differential Equations

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