I would like some help with this problem, please. (g) Supposethatr₁ (0) =< 3,2,1 >, r₂(0) = -1,2,3>, r₁(0) = 0,2,0 andr₂ (0) =< -5, -4,-2 >. Use this information to evaluate the derivative of each function att = 0.(i) r(t) = 2r₁(t) — r₂(t)(ii) r(t) = cos tri(t) + e²tr₂(t)(iii) r(t) = r₁(t) x r₂(t)(iv) f(t) = ri(t). r₂(t)

Answered: (g) Suppose that r₁ (0) =< 3, 2, 1 >,…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

I would like some help with this problem, please.

(g) Suppose
that
r₁ (0) =< 3,2,1 >, r₂(0) = -1,2,3>, r₁(0) = 0,2,0 and
r₂ (0) =< -5, -4,-2 >. Use this information to evaluate the derivative of each function at
t = 0.
(i) r(t) = 2r₁(t) — r₂(t)
(ii) r(t) = cos tri(t) + e²tr₂(t)
(iii) r(t) = r₁(t) x r₂(t)
(iv) f(t) = ri(t). r₂(t)

Expert Solution

Step 1: Problem

We are given:

$r subscript 1 open parentheses 0 close parentheses equals open angle brackets 3 comma 2 comma 1 close angle brackets comma space r subscript 2 open parentheses 0 close parentheses equals open angle brackets negative 1 comma 2 comma 3 close angle brackets comma space r apostrophe subscript 1 open parentheses 0 close parentheses equals open angle brackets 0 comma 2 comma 0 close angle brackets space a n d space r apostrophe subscript 2 open parentheses 0 close parentheses equals open angle brackets negative 5 comma negative 4 comma negative 2 close angle brackets. text We need to find the derivative of given r end text open parentheses t close parentheses text at t=0. This can be evaluated as follows: end text$