   Chapter 12.2, Problem 81E

Chapter
Section
Textbook Problem

# True or False? In Exercises 73-76, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. d d t [ ‖ r ( t ) ‖ ] = ‖ r ' ( t ) ‖

To determine
Whether the statement “ddt[r(t)]=r(t)” is true or false.

Explanation

The provided statement “The definite integral of a vector-valued function is a real number” is false.

Take an example.

Let r(t)=ti+t2j.

Now, find the magnitude of given vector,

r(t)=t2+t4=t1+t2

Again, differentiate the vector,

r(t)=i+2tj.

Also, Magnitude is:

r(t)=1+4t2

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