   Chapter 12.1, Problem 69E

Chapter
Section
Textbook Problem

# Continuity of a Vector-Valued Function In Exercises 69–74, determine the interval(s) on which the vector-valued function is continuous. r ( t ) = t i + 1 t j

To determine

To calculate: The interval on which vector valued function, r(t)=ti+1tj is continuous.

Explanation

Given:

The vector valued function is: r(t)=ti+1tj.

Formula used:

A vector value function, r is continuous at the point given by t=a when the limit of r(t) exist at ta.

limtr(t)=r(a)

A vector value function r is continuous on an interval I, when it is continuous at every point on the interval.

Calculation:

Consider the provider vector value function,

r(t)=ti+1tj.

Compare the above equation with the standard equation r(t)=f(t)i+g(t)j

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