Chapter 1.1, Problem 49E

(a)

To determine

To calculate: Estimate the limits

Answer to Problem 49E

The limit is $4$ .

Explanation of Solution

Given information: The limit $\underset{x\to 0^{-}}{\lim }F(x)$

Calculation:

The function reaches point 4 as the graph $F(x)$ moves left toward 0.

  $\underset{x\to 0^{-}}{\lim }F(x)=4$

Therefore the required limit is 4.

(b)

To determine

To calculate: Estimate the limits

Answer to Problem 49E

The limit is $-3$ .

Explanation of Solution

Given information: The limit is $\underset{x\to 0^{+}}{\lim }F(x)$

Calculation:

Trace the graph will reveal that it approaches the point $(0,-3)$ since $x=0$ from the right, meaning that the limit is -3.

Therefore, the required limit is -3.

(c)

To determine

To calculate: Estimate the limits

Answer to Problem 49E

The limit does not exists.

Explanation of Solution

Given information: The limit $\underset{x\to 0^{-}}{\lim }F(x)$

Calculation:

From 49a and 49b:

  $\begin{array}{c}\underset{x\to 0^{-}}{\lim }F(x)=4\\ \underset{x\to 0^{+}}{\lim }F(x)=-3\end{array}$

As there are distinct limitations on each side, there is no such thing as a limit.

Therefore, the required limit does not exists.

(d)

To determine

To calculate: Estimate the limits

Answer to Problem 49E

.The limit is 4.

Explanation of Solution

Given information: The limit $F(0)$

Calculation:

The $y$ -coordinate of the place where $x=0$ is located is equal to $F(0)$

At $x=0$ There is a filled/solid dot at (0,4), and its $y$ -coordinate is 4. $F(0)=4$ herefore the required limit is 4.