# To find the value of each quantity if it does not exist explain why.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2.2, Problem 6E

a.

To determine

## To find the value of each quantity if it does not exist explain why.

Expert Solution

4

### Explanation of Solution

Given:

limx3h(x)

Calculation:

The given graph is

limx3h(x)

As x approaches -3 from the left, h(x) approaches 4

b.

To determine

Expert Solution

4

### Explanation of Solution

Given:

limx3+h(x)

Calculation:

The given graph is

limx3+h(x)

As x approaches -3 from the left, h(x) approaches 4

c.

To determine

Expert Solution

4

### Explanation of Solution

Given:

limx3h(x)

Calculation:

The given graph is

limx3h(x)

As x approaches -3 from the left, h(x) approaches 4

d.

To determine

Expert Solution

4

### Explanation of Solution

Given:

h(3)

Calculation:

The given graph is

h(3)

As x approaches -3 from the left, h(x) approaches 4

e.

To determine

Expert Solution

1

### Explanation of Solution

Given:

limx0h(x)

Calculation:

The given graph is

limx0h(x)

Looking at the graph, we can see that the function approaches (and actually reaches) 1 as x approaches 0 from the left side.

f.

To determine

Expert Solution

1

### Explanation of Solution

Given:

limx0+h(x)

Calculation:

The given graph is

limx0+h(x)

Looking at the graph, we can see that the function approaches (and actually reaches) 1 as x approaches 0 from the right side.

g.

To determine

Expert Solution

Doesn’t exist.

### Explanation of Solution

Given:

limx0h(x)

Calculation:

The given graph is

limx0h(x)

Since the left hand limit and the right hand limit are not equal, the limit doesn’t exist.

h.

To determine

Expert Solution

1

### Explanation of Solution

Given:

h(0)

Calculation:

The given graph is

h(0)

h(0)=1

i.

To determine

Expert Solution

2

### Explanation of Solution

Given:

limx2h(x)

Calculation:

The given graph is

limx2h(x)

As x approaches 2 from the left, h(x) approaches 2

j.

To determine

Expert Solution

2

### Explanation of Solution

Given:

h(2)

Calculation:

The given graph is

h(2)=2

As x approaches 2 , h(x) approaches 2

k.

To determine

Expert Solution

3

### Explanation of Solution

Given:

limx5+h(x)

Calculation:

The given graph is

limx5+h(x)

As x approaches 5 from the right, h(x) approaches 3

l.

To determine

Expert Solution

Does not exist.

### Explanation of Solution

Given:

limx5h(x)

Calculation:

The given graph is

limx5h(x)

The behavior of the graph is not clear when x approaches 5 from left.

Hence limit doesn’t exist.

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