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Engineering Calculus Notes 206

Engineering Calculus Notes 206 - 194 CHAPTER 2 CURVES(d...

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194 CHAPTER 2. CURVES (d) Show that −→ p ( θ ) and −→ q ( σ ) cannot be reparametrizations of each other. ( Hint: Consider short open intervals about each of the parameter values where the origin is crossed, and show that their images under −→ p ( θ ) cannot match those under −→ q ( σ ).) History note: 15. Bolzano’s curve: A version of the following was constructed by Bernhard Bolzano (1781-1848) in the 1830’s; a fuller study is given in ( Calculus Deconstructed , § 4.11). (a) Start with the following: suppose we have an affine function
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