# The value of lim x → ∞ f ( x ) . ### 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 2.5, Problem 3E

(a)

To determine

## To find: The value of limx→∞f(x).

Expert Solution

The value of limxf(x)=2.

### Explanation of Solution

From the given graph, it is observed that the curve approaches 2 as x approaches infinity from either side.

(b)

To determine

### To find: The value of limx→−∞f(x).

Expert Solution

The value of limxf(x)=2.

### Explanation of Solution

From the given graph, it is observed that the curve approaches 2 as x approaches negative infinity from either side.

(c)

To determine

### To find: The value of limx→1f(x).

Expert Solution

The value of limx1f(x)=.

### Explanation of Solution

From the given graph, it is observed that the curve approaches infinity as x approaches 1 from either side.

(d)

To determine

### To find: The value of limx→3f(x).

Expert Solution

The value of limx3f(x)=.

### Explanation of Solution

From the given graph, it is observed that the curve approaches as x approaches 3 from either side.

(e)

To determine

### To find: The equations of the asymptotes.

Expert Solution

Solution: The equations of the asymptote are x=1,x=3,y=2 and y=2.

### Explanation of Solution

Recall the definition that the line x=a is said to be a vertical asymptote of the function f(x), if either limxaf(x)=± or limxa+f(x)=±.

Recall the definition that the line x=a is said to be a horizontal asymptote of the function f(x), if either limx±f(x)=a or limx±f(x)=a.

From the limits obtained from the parts (a)-(d), it can be concluded that the equations of asymptote are x=1,x=3,y=2 and y=2.

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