| ucf24-006 Find the domain and range of the following functions:
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| ucf25-002 For each of the following sets of parametric equations: (i) Graph in the x-y plane. (Caution: they are all different graphs.) (ii) What do these graphs have in common? (iii) Show how each graph is traced as values of \( t \) go from \( -\infty \) to 0 to \( +\infty \) .
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| ucf25-004 Consider the parametric equations \( x(t) = e^{t }+ e^{-t} , y(t) = e^{t }- e^{-t} \) .
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| ucf26-001 For the following sets of parametric equations, sketch the curve in the x-y plane, and find for what values of \( t \) (if any) the slope is \( 0 , \pm 1 ,\text{ or }\infty \) .
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| ucf26-003 For the following curves, i) Find the curvature as a function of \( x \). ii) Find the maximum values of the curvature. iii) Find the minimum values of the curvature. iv) Sketch the circle of curvature at the points of ii).
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