   Chapter 12.2, Problem 30E

Chapter
Section
Textbook Problem

# Finding Intervals on Which a Curve Is Smooth In Exercises 29–38, find the open interval(s) on which the curve given by the vector-valued function is smooth. r ( t ) = 1 t − 1 i + 3 t j

To determine

To calculate: The open intervals on which the curve given by the vector-valued function r(t)=1t1i+3tj is smooth.

Explanation

Given:

The vector-valued function,

r(t)=1t1i+3tj

Calculation:

The curve represented by a vector-valued function,

r(t)=f(t)i+g(t)j+h(t)k is smooth on an open-interval I when f, g and h are continuous on I and r(t)0 for any t in the interval I.

Consider the vector-valued function,

r(t)=1t1i+3tj

Differentiate the above function component-by-component to get the derivative as,

r(t)=1(t1)2i<

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