Answer to Question #228911 in Calculus for fouzi

Question

 Find the domain of r(t) and the value of r(t0).1, t 2; t0 = 1

Answer 1

$$\vec r(t)=\langle t^2,\dfrac{1}{t}, \sqrt{1-t}\rangle$$

$$t\not=0, 1-t\geq0$$

$Domain: (\infin, 0)\cup(0, 1]$

$t_0=1$

$$\vec r(t_0)=\vec r(1)=\langle 1^2,\dfrac{1}{1}, \sqrt{1-1}\rangle$$

$$=\langle 1,1, 0\rangle$$

$$\vec r(t_0)=\vec r(1)=\vec i+\vec j$$