Domain and Continuity In Exercises 1-4, (a) find the domain of r, and (b) determine the interval(s) on which the function is continuous.
(a)
To calculate: The domain of the function
Answer to Problem 1RE
Solution:
The domain is
Explanation of Solution
Given:
The vector-valued function is
Calculation:
Consider the function:
The x-coordinate of the function cannot be zero. Thus,
Where n is integer.
Thus, the required domain is
(b)
To calculate: The interval on which the function
Answer to Problem 1RE
Solution:
The function is continuous for all
Explanation of Solution
Given:
The function
Calculation:
Consider the function:
Evaluate the continuity of the vector valued function by evaluating the continuity of the component functions and then taking the intersection of the two sets.
The component functions of the vector valued function are:
Both the functions g and h are continuous for all real values of t.
However, the function f is continuous for
Where n is an integer.
Therefore, the function is continuous for
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Calculus
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