Graphing a calculus problem involving limits on Mathematica

Questions
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1

Hey all, I’ve spent a few hours trying to graph the following Calculus problem on Mathematica but I’ve struggled to find the right code…

Screenshot2023-10-02at10.17.42PM.png
Screenshot2023-10-02at10.17.42PM.png1078×822 69.1 KB

I was trying to use the Manipulate command somehow to control the radius of C2 in order to see the coordinate of R shift. I basically just want to do what this person did on geogebra (Stewart Ejercicio de límites – GeoGebra) but on Mathematica instead.

2

Here is an attempt:

pointP[s_] = {0, s};
Assuming[0 < s < 2,
  pointQ[s_] = SolveValues[{x, y} \[Element] Circle[{0, 0}, s] &&
      {x, y} \[Element] Circle[{1, 0}, 1] &&
      y > 0,
     {x, y}][[1]];
  pointR[s_] = SolveValues[{x, y} \[Element] InfiniteLine[{pointQ[s],
         pointP[s]}] &&
      y == 0,
     {x, y}][[1]]];
Manipulate[Graphics[{Circle[{0, 0}, r], Circle[{1, 0}, 1],
   PointSize[Large], Point[{pointQ[r], pointP[r], pointR[r]}], 
   InfiniteLine[{pointQ[r], pointP[r]}]},
  Axes -> True, PlotRange -> {{-2, 4.5}, {-2, 3}}],
 {{r, 3/2}, 0, 2}]
3

Gonna try this again brb

4

Woah you got it! This is definitely a complex code, I wouldn’ve never been been able to figure it out haha. Thank you!