   Chapter 12.2, Problem 32E

Chapter
Section
Textbook Problem

# Finding Intervals on Which a Curve Is Smooth In Exercises 27-34, find the open interval(s) on which the curve Riven by the vector- valued function is smooth. r ( θ ) = ( θ + sin θ ) i + ( 1 − cos θ ) j , 0 ≤ θ ≤ 2 π

To determine

The interval on which the curve r(θ)=(θ+sinθ)i+(1cosθ)j is smooth.

Explanation

Given:

The provided vector valued function is r(θ)=(θ+sinθ)i+(1cosθ)j, 0θ2π

Explanation:

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

r'(θ)=(1+cosθ)i+sinθjfor smooth curve r'(θ)=0(1+cosθ)

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