(a)
To find: Whether the given curve has vertical asymptotes or horizontal asymptotes.
(a)
Answer to Problem 6RCC
The given curve has no asymptotes.
Explanation of Solution
Result used:
Definition of vertical asymptote:
The vertical asymptote of the function
Limit is defined as
Definition of horizontal asymptote:
The horizontal asymptote of the function
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 find: Whether the curve y = sin x have vertical asymptotes or horizontal asymptotes.
(b)
Answer to Problem 6RCC
The graph of y = sin x has no asymptotes.
Explanation of Solution
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 find: Whether the curve y = tan x have vertical asymptotes or horizontal asymptotes.
(c)
Answer to Problem 6RCC
There are only vertical asymptotes at
Explanation of Solution
Graph:
The graph of a function
Calculation:
For horizontal asymptotes,
There are no horizontal asymptotes.
From the graph there are vertical asymptotes at
(d)
To find: Whether the given curve has vertical asymptotes or horizontal asymptotes
(d)
Answer to Problem 6RCC
There are only horizontal asymptotes at
Explanation of Solution
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 find: Whether the given curve has vertical asymptotes or horizontal asymptotes
(e)
Answer to Problem 6RCC
There are only horizontal asymptote at
Explanation of Solution
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 find: Whether the given curve has vertical asymptotes or horizontal asymptotes.
(f)
Answer to Problem 6RCC
There are only vertical asymptote at
Explanation of Solution
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 find: Whether the given curve has vertical asymptotes or horizontal asymptotes
(g)
Answer to Problem 6RCC
There is vertical asymptote at
There is horizontal asymptote at
Explanation of Solution
Graph:
The graph of a function
Calculation:
There is horizontal asymptote at
That is
There is vertical asymptote at
That is
(h)
To find: Whether the given curve has vertical asymptotes or horizontal asymptotes.
(h)
Answer to Problem 6RCC
The given curve has no asymptotes.
Explanation of Solution
Graph:
The graph of a function
Calculation:
For vertical asymptotes,
There are no vertical asymptotes.
For horizontal asymptotes:
There are no horizontal asymptotes.
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition