Chapter 11, Problem 2PS

(a)

To determine

To Graph: The function $f\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}\sqrt{t^4+1}dt}$ on the interval $-2\le x\le 2$.

(b)

To determine

To calculate: A unit vector parallel to the graph of $f\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}\sqrt{t^4+1}dt}$ at the point $\left(0,0\right)$.

(c)

To determine

To calculate: A unit vector perpendicular to the graph of $f\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}\sqrt{t^4+1}dt}$ at the point $\left(0,0\right)$.

(d)

To determine

To calculate: The parametric equations of the tangent line to the graph of $f\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}\sqrt{t^4+1}dt}$ at the point $\left(0,0\right)$.