Use the theorem on the Stability of Equilibrium Points to determine the stability of the equilibrium...

 

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Use the theorem on the Stability of Equilibrium Points to determine the stability of the equilibrium points O and 1 and how they depend on r. Determine the stability of the equilibrium point x = 0 and how the stability depends on r. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The equilibrium point 0 is unstable for all r. B. The equilibrium point 0 is stable for 0<r< and unstable for r> C. The equilibrium point 0 is unstable for D. The equilibrium point 0 is unstable for 0<r< <r< and stable forr< and r> and stable for r> E. The equilibrium point 0 is stable for <r< and unstable for r< and r> O F. The equilibrium point 0 is stable for all r. Use the theorem on the Stability of Equilibrium Points to determine the stability of the equilibrium points O and 1 and how they depend on r. Determine the stability of the equilibrium point x = 0 and how the stability depends on r. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The equilibrium point 0 is unstable for all r. B. The equilibrium point 0 is stable for 0<r< and unstable for r> C. The equilibrium point 0 is unstable for D. The equilibrium point 0 is unstable for 0<r< <r< and stable forr< and r> and stable for r> E. The equilibrium point 0 is stable for <r< and unstable for r< and r> O F. The equilibrium point 0 is stable for all r.

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