Finding tangents using old methods: Fermat’s Barrow’s and Newton’s Methods, assignment help

  

This is or a history of math class. These need to be solved using the specific methods being asked. I will upload the file with the questions. I also have filed with the pages mentioned in the worksheet, I will upload those when I find a tutor.
problems.pdf

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Problem Set M: Finding Tangents
This problem set concerns various techniques for constructing tangents.
1. The method of composition of motions was used to …nd tangents to such
curves as ellipses, parabolas, hyperbolas, and cycloids. Let P and Q be the
points (1; 0) and ( 1; 0). Let X be any point, and de…ne f (X) to be the
distance from X to P plus twice the distance from X to Q. Consider the curve
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C consisting of those points X for which f (X) = 13
2 . The point Y = (1; 2 ) lies
on C. Use the method of composition of motions to …nd the slope of the tangent
to C at Y .
2. Use Fermat’s method for computing tangents (described on pp. 391–392) to
…nd the equation of the tangent to the curve x3 + y 3 = 9 at the point (1; 2).
3. Use Barrow’s method for computing tangents (pp. 395–396) to …nd the
equation of the tangent to the curve x3 + y 3 = 29 xy at the point (1; 2).
4. Use Newton’s method of ‡uxions (see pp. 400–401) to …nd the equation of
the tangent to the curve x4 + y 3 = 9 at the point (1; 2).
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