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) =

Q: Find the points on the curve c where the tangent is vertical C: x= t - 48t, y = t + 12t. ОА (-128,…

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Q: b) For the curve 2² - 4ry² = y³ +9, do the following:

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Q: Find all x values on the function y = B x²+x+2 where there is a horizontal tangent. M

A: To find the horizontal tangent for given function

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Q: ts (2,9) and (8,-1), exact distance between the.

A: The given points are 2,9 and 8, -1. We have to find the distance between the points.

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Q: Q5/ Find the equation of the circle tangent to the lines y=2, x-3 and y = x+2.

A: Explained below

Q: Find the length of the arc of this curve and Sketch the curve y cu. = x sq.  from ( -1,1 ) and ( 8,4…

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Q: Sketch the curve of the following:  y = ∛x3 + 1  (everything except the y is under the ∛ symbol)…

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Q: What about the part where it has to be part of the curve r= sqrt(2cos(2theta))?

A: As per the question to evaluate the volume of a cylinder with specific geometric properties, we can…

Q: Find a function γ that describes the circle of radius 3 centered at z = 3 - 2i.

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