Chapter 2.3, Problem 10E

To determine

To find:The points of continuity and discontinuity of the function $y=\ln \left(x+1\right)$ . Also,write the type of each discontinuity.

Answer to Problem 10E

The function $y=\ln \left(x+1\right)$ is continuous for all the values of $x$ except $x\le -1$ .

Explanation of Solution

Given information:The functionis $y=\ln \left(x+1\right)$ .

Calculation:

To graph a function $y=\ln \left(x+1\right)$ , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press $\boxed{\text{Y}=}$ key and enter right hand side of the equation $y=\ln \left(x+1\right)$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{\text{LN}}\boxed{\text{X}}\boxed{+}\boxed{1}\boxed{)}$ .

The display will show the equation,

  ${\text{Y}}_{\text{1}}=\ln \left(\text{X}+1\right)$

Now, press the $\boxed{\text{GRAPH}}$ key and $\boxed{\text{TRACE}}$ key to produce the graph of given function in standard window as shown below.

  

Figure(1)

As observed from graph, the function $y=\ln \left(x+1\right)$ is continuous at every point of $x$ in the domain that is $x\ge -1$ . So, the function $y=\ln \left(x+1\right)$ is discontinuous for every value of $x\le -1$ .

Therefore, the function $y=\ln \left(x+1\right)$ is continuous for all the values of $x$ except $x\le -1$ .