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10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

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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 determine

**To calculate:** The domain of the function

Answer

**Solution:**

The domain is *n* is integer.

Explanation

**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 *n* is integer.

**(b)**

To determine

**To calculate:** The interval on which the function

Answer

**Solution:**

The function is continuous for all *n* is integer.

Explanation

**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 *n* is an integer.

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