   Chapter 12.2, Problem 7E

Chapter
Section
Textbook Problem

# Differentiation of Vector-Valued FunctionsIn Exercises 3–10, find r t ( t ) , r ( t 0 ) , and r t ( t 0 ) for the given value of t 0 . Then sketch the curve represented by the vector-valued function and sketch the vectors r ( t 0 ) and r t ( t 0 ) . r ( t ) = 2 cos t i + 2 sin t j + t k ,     t 0 = 3 π 2

To determine
The value of function r'(t), r(t0), r'(t0) at given value of t0 and sketch the vector valued function and also sketch the vectors r(t0), r'(t0). r'(t), r'(t0), r(t0) and their graphs.

Explanation

Given:

The provided vector-valued function is r(t)=2costi+2sintj+tk, t=3π2

Explanation:

The derivative of the given function is:

r'(t)=2sinti+2costj+k [as ddtsint=cost and ddtcost=sint ]r'(3π2)=2sint3π2i+2cos3π2i+k=2i+k; r(3π2)=2j+(3π2

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