Chapter 1.2, Problem 6E

a.

To determine

To find: The third Taylor polynomial $P_3\left(x\right)$ about $x_0=0$ for the function $f\left(x\right)=\sqrt{x+1}$ .

b.

To determine

To find: The approximate value of $\sqrt{0.5}$ , $\sqrt{0.75}$ , $\sqrt{1.25}$ , and $\sqrt{1.5}$ using $P_3\left(x\right)$ .

c.

To determine

To find: The actual error of the approximations of $\sqrt{0.5}$ , $\sqrt{0.75}$ , $\sqrt{1.25}$ , and $\sqrt{1.5}$ .