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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2, Problem 6RCC

(a)

To determine

**To find:** Whether the given curve has vertical asymptotes or horizontal asymptotes.

Expert Solution

The given curve has no asymptotes.

**Result used:**

**Definition of vertical asymptote:**

The vertical asymptote of the function *y* approaches *x* approaches *a* from the right or left.

Limit is defined as

**Definition of horizontal asymptote:**

The horizontal asymptote of the function *y* approaches *b* as *x* approaches

Limit is defined as

**Graph:**

The graph of a function

**Calculation:**

For vertical asymptotes:

There are no vertical asymptotes.

For horizontal asymptotes:

There are no horizontal asymptotes.

(b)

To determine

**To find:** Whether the curve *y* = sin *x* have vertical asymptotes or horizontal asymptotes.

Expert Solution

The graph of *y* = sin *x* has no asymptotes.

The graph of a function

There are no vertical asymptotes, because the function

For vertical asymptotes:

There are no vertical asymptotes.

For horizontal asymptotes:

There are no horizontal asymptotes, because from the graph the function

(c)

To determine

**To find:** Whether the curve *y* = tan *x* have vertical asymptotes or horizontal asymptotes.

Expert Solution

There are only vertical asymptotes at

**Graph:**

The graph of a function

**Calculation:**

For horizontal asymptotes,

There are no horizontal asymptotes.

From the graph there are vertical asymptotes at *n* = 0,1,2,3,…

(d)

To determine

**To find:** Whether the given curve has vertical asymptotes or horizontal asymptotes

Expert Solution

There are only horizontal asymptotes at

**Graph:**

The graph of a function

**Calculation:**

For vertical asymptotes,

There are no vertical asymptotes.

From the graph there are horizontal asymptotes at

(e)

To determine

**To find:** Whether the given curve has vertical asymptotes or horizontal asymptotes

Expert Solution

There are only horizontal asymptote at

**Graph:**

The graph of a function

**Calculation:**

For vertical asymptotes,

There are no vertical asymptotes.

From the graph there are horizontal asymptote at

(f)

To determine

**To find:** Whether the given curve has vertical asymptotes or horizontal asymptotes.

Expert Solution

There are only vertical asymptote at

**Graph:**

The graph of a function

**Calculation:**

For horizontal asymptotes,

There are no horizontal asymptotes

From the graph there is vertical asymptote at

(g)

To determine

**To find:** Whether the given curve has vertical asymptotes or horizontal asymptotes

Expert Solution

There is vertical asymptote at

There is horizontal asymptote at

**Graph:**

The graph of a function

**Calculation:**

There is horizontal asymptote at

That is

There is vertical asymptote at

That is

(h)

To determine

**To find:** Whether the given curve has vertical asymptotes or horizontal asymptotes.

Expert Solution

The given curve has no asymptotes.

**Graph:**

The graph of a function

**Calculation:**

For vertical asymptotes,

There are no vertical asymptotes.

For horizontal asymptotes:

There are no horizontal asymptotes.