In the following questions the domain of all vector fields will be taken as f? =...

 

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In the following questions the domain of all vector fields will be taken as f? = R. Show that the curves n(t)= (Rsint, R cost) for a fixed R20 are integral curves for the vector field X = (y. -z). Sketch these curves on a diagram, indicating any critical points of X and indicating with an arrow the direction of increasing parameter for each sketched integral curve. In the following questions the domain of all vector fields will be taken as f? = R. Show that the curves n(t)= (Rsint, R cost) for a fixed R20 are integral curves for the vector field X = (y. -z). Sketch these curves on a diagram, indicating any critical points of X and indicating with an arrow the direction of increasing parameter for each sketched integral curve.