The direction field for the differential equation indicates that slopes are positive when

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

Problem

The direction field for the differential equation dydx=y(1−y5)\dfrac{dy}{dx}=y\left(1-\dfrac{y}{5}\right) indicates that slopes are positive when 0<y<50<y<5 and negative when y>5y>5. For the solution satisfying y(0)=1y(0)=1, what is lim⁡x→∞y(x)\displaystyle \lim_{x\to\infty} y(x)? (a) 00 (b) ∞\infty (c) 55 (d) 2.52.5

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