To set up our curve in Mathematica, run the following: R=5; r[t_]:={R*Cos [t], R*Sin[t], t} (We could have omitted R and just typed 5, I just wanted to give you "flexible code" which can be adjusted to other radii.) See if you can do the following derivatives in Mathematica using the single apostrophe symbol: r' [t] r''[t] Try this in Mathematica, using either. or the Dot command we have seen before. Fully simplify each answer-keep in mind the Pythagorean identity cos²(t) + sin²(t) = 1. You can also end your commands with //FullSimplify. r' (t) r(t) = 1+25Cos[t]^2+25sin[t]^2 r" (t) r(t) = 25Cos[t]^2+25sin[t]^2 r¹(t).r"(t) =

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