Chapter 12, Problem 5RE

(a)

To determine

To calculate: The value of $r\left(0\right)$ for the vector-valued function $r\left(t\right)=\left(2t+1\right)i+t^{2}j-\sqrt{t+2}k$.

(b)

To determine

To calculate: The value of $r\left(-2\right)$ for the vector-valued function, $r\left(t\right)=\left(2t+1\right)i+t^{2}j-\sqrt{t+2}k$.

(c)

To determine

To calculate: The value of $r\left(c-1\right)$ for vector-valued function $r\left(t\right)=\left(2t+1\right)i+t^{2}j-\sqrt{t+2}k$.

(d)

To determine

To calculate: The value of $r\left(1+\Delta t\right)-r\left(1\right)$ for vector-valued function $r\left(t\right)=\left(2t+1\right)i+t^{2}j-\sqrt{t+2}k$ at $t=1+\Delta t$ and $t=1$.