   Chapter 12.1, Problem 79E

Chapter
Section
Textbook Problem

# Writing a Transformation In Exercises 75–78, consider the vector-valued function r ( t ) = t 2 i + ( t − 3 ) j + t k . Write a vector-valued function s(t) that is the specified transformation of r.Continuity of a Vector-Valued Function State the definition of continuity of a vector-valued function. Give an example of a vector-valued function that is defined but not continuous at t = 2.

To determine

Definition of continuity of a vector value function and also give an example of a vector value function that is defined but not continuous at t=2.

Explanation

The continuity of a vector value function is defined as,

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. Where, I is the interval within the domain of the vector value function.

Example- let a vector value function, r(t)={   i+j,  t2i+j,  t<2.

Check the continuity of the vector value function at t=2

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