   Chapter 12, Problem 6RE

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# Evaluating a FunctionIn Exercises 5 and 6, evaluate the vector-valued function at each given value of t . r ( t ) = 3 cos t i + ( 1 − sin t ) j − t k (a) r ( 0 ) (b) r ( π 2 ) (c) r ( s − π ) (d) r ( π + Δ t ) − r ( π )

(a)

To determine

To calculate: The value of r(0) for vector-valued function r(t)=3costi+(1sint)jtk.

Explanation

Given:

The vector-valued function is:

r(t)=3costi+(1sint)jtk

Calculation:

Consider the following vector valued function:

r(t)=3costi+(1sint)jt

(b)

To determine

To calculate: The value of r(π2) for vector-valued function r(t)=3costi+(1sint)jtk.

(c)

To determine

To calculate: The value of r(sπ) for vector-valued function r(t)=3costi+(1sint)jtk.

(d)

To determine

To calculate: The value of r(π+Δt)r(π) for the vector-valued function r(t)=3costi+(1sint)jtk.

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