Chapter 12, Problem 1RE

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
315 views

# 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. r ( t ) = tan t i + j + t k

(a)

To determine

To calculate: The domain of the function r(t)=tanti+j+tk.

Solution:

The domain is tπ2+nπ, n is integer.

Explanation

Given:

The vector-valued function is r(t)=tanti+j+tk.

Calculation:

Consider the function:

r(t)=tanti+j+tk

The x-coordinate of the function cannot be zero. Thus,

tant0tπ2+nπ

Where n is integer.

Thus, the required domain is tπ2+nπ, n is integer.

(b)

To determine

To calculate: The interval on which the function r(t)=tanti+j+tk is continuous.

Solution:

The function is continuous for all tπ2+nπ, n is integer.

Explanation

Given:

The function r(t)=tanti+j+tk.

Calculation:

Consider the function:

r(t)=tanti+j+tk

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:

f(t)=tant,g(t)=1,h(t)=t

Both the functions g and h are continuous for all real values of t.

However, the function f is continuous for

tant0tπ2+nπ

Where n is an integer.

Therefore, the function is continuous for tπ2+nπ, where n is an integer.

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