a) Find the value of c for which the curves y = ln x and y = cx² are tangent to each other. b) Find the value of c for which the curves y = ln x and y = cx² are orthogonal to each other. c) Plot the functions from part a) in the domain x € [0.1, 5] and from part b) in the window x E [0.1, 5], y E [–2,3].
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