Chapter 4.7, Problem 2E

Follow the instructions for Exercise 1(a) but use x₁ = 1 as the starting approximation for finding the root r.

To determine

To draw: The graph of a tangent line at $x_1=6$ and estimate the numerical value of $x_2$ and $x_3$ from graph.

Answer to Problem 2E

The numerical value of $x_2$ and $x_3$ is $\underset{\_}{3.5}$ and $\underset{\_}{2.8}$.

Explanation of Solution

At first draw the tangent line at the point $x_1=1$ and the tangent line intersect the $x$ -axis. Let the intersecting point be $x_2$.

Similarly, draw the tangent line at the point $x_2=3.5$ and the tangent line intersect the $x$-axis. Let that intersecting point be $x_3$.

Graph:

Observation:

From Figure 1, it is observed that the value of $x_2$ is equal to $3.5$ and $x_3$ is equal to $2.8$ and also observed that the value of $x_3$ is close to the value of $r$.

Thus, the value of $x_2$ and $x_3$ is $\underset{\_}{3.5}$ and $\underset{\_}{2.8}$ and the value of $x_3$ is close to the value of $r$.