Chapter 11, Problem 2PS

(a)

To determine

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

(b)

To determine

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

(c)

To determine

To calculate: The 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 $\left(0,0\right)$.