Please answer all parts Thank You 5. Find the length of the curve• r(t) = cos(t)i+sin(t)j + ln(cos(t))k6. Use the Chain Rule to find the indicated partial derivative• w=xy+yz+zx, x=rcos (0), y=rsin(0), z=r0;we when r = 2, 0 = π/27. Find the directional derivative of the function at the given point in the direction of thevector v●0≤t≤π/4f(x, y, z)= xey + ye²+zet, (0,0,0) v = (5,1, -2)

since you have posted multiple question in this question which are not interlinked so i have solved…

Answered: 5. Find the length of the curve • r(t)…

Math

Calculus

5. Find the length of the curve • r(t) = cos(t)i + sin(t)j +ln(cos(t))k 0≤t≤n/4

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

Please answer all parts Thank You

5. Find the length of the curve
• r(t) = cos(t)i+sin(t)j + ln(cos(t))k
6. Use the Chain Rule to find the indicated partial derivative
• w=xy+yz+zx, x=rcos (0), y=rsin(0), z=r0;
we when r = 2, 0 = π/2
7. Find the directional derivative of the function at the given point in the direction of the
vector v
●
0≤t≤π/4
f(x, y, z)= xey + ye²+zet, (0,0,0) v = (5,1, -2)

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