   Chapter 12.2, Problem 37E

Chapter
Section
Textbook Problem

# Finding Intervals on Which a Curve Is SmoothIn Exercises 27–34, find the open interval(s) on which the curve given by the vector-valued function is smooth. r ( t ) = t i − 3 t j + tan t k

To determine
The interval on which the curve r(t)=ti3tj+tantk is smooth.

Explanation

Given:

The provided vector valued function is r(t)=ti3tj+tantk

Explanation:

The curve become smooth when r'(t)=0.

Differentiate the function

r'(t)=i3j+sec2tkHence, r'(t)0 for any t

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