G.3) Splines in road design D G.3.A) How are two straight roads conning parallel to each other together with specially marked points at [-3. -1) and =: [3. 1): Clour [high, low, x]: high [x_] = 1; low[x_] . -1; readn . Flet[(high[x], low[=]), {x, -4, 4]. FlatStyle + ((GrayLaval[0.6], Chicknamm [0.021 1, (GrayLaval 10.6], Chicknans [0-021}}, Axantabal + {"x", ""). PlotMango + (-2, 3), Epilog - {{PointSize [0.04], Point [(-3, -1)1). [PointSism [0.04], Point [ (3, 1)1::1 X Design a smooth crossover that leaves the bowom road at [-3, -1), and connects to the cop road at (3. 1). For safety, make vone your crossover has at least order of comact 1 at both connections. Flow your crossover. This is not welike the toonal problem on landing aleplanes. G.3.bj Have are two ourned roads together with specially marked pokers at (-2, -3j and an (1, =]: Clour [high, low, x]; + 1; low[x_] . - 1: roudn . Flet[(high[x], low(=]], {x, -3, 3}, FlatStylo + {{GrayLaval[0.8], Thicknam [0-02]], {GrayLawal 10. 6], Chicknown [0.02]17, AxumCabal + ("x", "), Epilog - {{PointSix [0.04], Peint[ {-2, low[-2101), (Point Sism[0.04], Paint[(1, high(100]]]] -1 Design a smooth crossover that leaves the bowom road at [-2, -2), and connects to the cop road ax (1. =) . For safety, make sure your crossover has at least order of contact 1 at bock connections. Flot your crossover. G.4) Order of contact for derivatives and integrals* D G.4.al) Derivatives Tikce ([x] = x Sim[x]] and g(x! = x# Sin(x] and look ac Clanr [x, 5, a, k]; atz_ ] . =' sim[x]: Dubla[(D[f(=], {x, kil. >[a[x], {x. k)]] /. x->0, {k, 0, 630