Given $x^{2/3}+y^{2/3}=1$, we can solve for $y$ and find two functions. In terms of nomenclature, do we have one or two parametrizations of the curve?

score 52 · Answer 13 · 2022-06-05 04:23:06

Spivak, Ch 12 Appendix, Prob. 5: Parametric curve $(u(t),v(t))$. Show line from furthest point Q on curve to point P is perpendicular to tangent at Q.

score 136 · Answer 14 · 2022-06-06 18:02:29

136

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How to compute $\lim\limits_{\theta \to \frac{\pi}{2}^+} \frac{\cos{\theta}-2\sin{\theta}\cos{\theta}}{\sin^2{\theta}-\cos^2{\theta}-\sin{\theta}}$?

Published on 06 Jun 2022 - 18:02

score 56 · Answer 15 · 2022-06-07 01:13:38

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Spivak, Ch. 12 Appendix Problem 9: Prove that slope between two points on parametric curve equal to slope of tangent to point in between two points.

Published on 07 Jun 2022 - 1:13

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Given $x^{2/3}+y^{2/3}=1$, we can solve for $y$ and find two functions. In terms of nomenclature, do we have one or two parametrizations of the curve?

Spivak, Ch 12 Appendix, Prob. 5: Parametric curve $(u(t),v(t))$. Show line from furthest point Q on curve to point P is perpendicular to tangent at Q.

How to compute $\lim\limits_{\theta \to \frac{\pi}{2}^+} \frac{\cos{\theta}-2\sin{\theta}\cos{\theta}}{\sin^2{\theta}-\cos^2{\theta}-\sin{\theta}}$?

Spivak, Ch. 12 Appendix Problem 9: Prove that slope between two points on parametric curve equal to slope of tangent to point in between two points.

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