   Chapter 12.2, Problem 34E

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 given by the vector valued function is smooth. r ( t ) = 2 t 8 + t 3 i + 2 t 2 8 + t 3 j

To determine

To Calculate: The interval on which the curve r(t)=2t8+t3i+2t28+t3j is smooth

Explanation

Given:

The curve represented by vector valued function is;

r(t)=2t8+t3i+2t28+t3j

Calculation:

The derivative of r(t) is;

r'(t)=(8+t3)22t3t2(8+t3)2i+(8+t3)4t2t23t2(8+t3)2j=16+2t36t3(8+t3)2i+32+4t46t4(8+t3)2j=164t3(8+t3<

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