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1. Check that a curve x=cosht, y=sinht becomes a hyperbola. Draw its graph, and calculate its...

1. Check that a curve x=cosht, y=sinht becomes a hyperbola. Draw its graph, and calculate its curvature.

2. Let a be a positive constant number. Draw the graph of a catenary y=acosh(x/a). Calculate the arc length s from the point (0,a) to the point (x,acosh(x/a)), and find the expression of the curve in terms of the parameter s.

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