Chapter 2.1, Problem 47E

(a)

To determine

To find: The value of $\underset{h\to 0^{-}}{\lim }f\left(h\right)$ with the help of graph.

Answer to Problem 47E

The value of $\underset{h\to 0^{-}}{\lim }f\left(h\right)$ is equal to $-4$ .

Explanation of Solution

Given information:

The graph of the function is:

  

Calculation:

As shown in graph, the function $y=f\left(h\right)$ approaches to $-4$ as $h$ approaches to $0$ from the left side.

So, the left hand limit of $y=f\left(h\right)$ at $h=0$ is equal to $-4$ .

Therefore, the value of $\underset{h\to 0^{-}}{\lim }f\left(h\right)$ is equal to $-4$ .

(b)

To determine

To find: The value of $\underset{h\to 0^{+}}{\lim }f\left(h\right)$ with the help of graph.

Answer to Problem 47E

The value of $\underset{h\to 0^{+}}{\lim }f\left(h\right)$ is equal to $-4$ .

Explanation of Solution

Given information:

The graph of the function is:

  

Calculation:

As shown in graph, the function $y=f\left(h\right)$ approaches to $-4$ as $h$ approaches to $0$ from the right side.

So, the right hand limit of $y=f\left(h\right)$ at $h=0$ is equal to $-4$ .

Therefore, the value of $\underset{h\to 0^{+}}{\lim }f\left(h\right)$ is equal to $-4$ .

(c)

To determine

To find: The value of $\underset{h\to 0}{\lim }f\left(h\right)$ with the help of graph.

Answer to Problem 47E

The value of $\underset{h\to 0}{\lim }f\left(h\right)$ is $-4$ .

Explanation of Solution

Given information:

The graph of the function is:

  

Calculation:

As calculated in part (a) and part (b), the value of $\underset{h\to 0^{-}}{\lim }f\left(h\right)$ is equal to $-4$ and the value of $\underset{h\to 0^{+}}{\lim }f\left(h\right)$ is equal to $-4$ .

So, the value of both $\underset{h\to 0^{-}}{\lim }f\left(h\right)$ and $\underset{h\to 0^{+}}{\lim }f\left(h\right)$ are equal to $-4$ .

Therefore, the value $\underset{h\to 0}{\lim }f\left(h\right)$ is $-4$ .

(d)

To determine

To find: The value of $f\left(0\right)$ with the help of graph.

Answer to Problem 47E

The value of $f\left(0\right)$ is equal to $-4$ .

Explanation of Solution

Given information:

The graph of the function is:

  

Calculation:

As shown in graph, the value of function $y=f\left(h\right)$ is $-4$ at the point $h=0$ .

Therefore, the value of $f\left(0\right)$ is $-4$ .