Example 2-3-7 - Maple Help



Chapter 2: Space Curves



Section 2.3: Tangent Vectors



Example 2.3.7



Given the plane curve $C$ defined by $y\left(x\right)=\frac{1-{x}^{2}}{1+{x}^{2}}$,

 a) Obtain $\mathbf{R}\left(p\right)$, the radius-vector form of the curve, by the parametrization $x=p,y=y\left(p\right)$.
 b) Obtain $\mathbf{R}\prime \left(p\right),\mathrm{ρ}\left(p\right)$ and $\mathbf{T}\left(p\right)$, where $\mathrm{ρ}=∥\mathbf{R}\prime ∥$ and $\mathbf{T}=\mathbf{R}\prime /\mathrm{ρ}$.
 c) Graph $C$ and the vectors $\mathbf{R}\left(1\right)$ and $\mathbf{T}\left(1\right)$.
 d) Graph $\mathrm{ρ}\left(p\right),p\in \left[0,3\right]$, and determine the point $\left[x,y\right]$ at which $\mathrm{ρ}$ is a maximum in this interval.