Calculus Combo
Calculus Combo
14th Edition
ISBN: 9781464151088
Author: Associate Professor Laura Taalman, Peter Kohn
Publisher: W.H. Freeman & Company
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Chapter 3, Problem 6GFT
To determine

To write a formula for the volume of a right circular cylinder whose radius r is half of its height?

To determine

To write a formula for the surface area of a right circular cylinder whose radius r is half of its height?

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Question 4. Suppose you need to know an equation of the tangent plane to a surface S at the point P(2, 1, 3). You don't have an equation for S but you know that the curves r1(t) = (2 + 3t, 1 — t², 3 − 4t + t²) r2(u) = (1 + u², 2u³ − 1, 2u + 1) both lie on S. (a) Check that both r₁ and r2 pass through the point P. 1 (b) Give the expression of the 074 in two ways Ət ⚫ in terms of 32 and 33 using the chain rule მყ ⚫ in terms of t using the expression of z(t) in the curve r1 (c) Similarly, give the expression of the 22 in two ways Əz ди ⚫ in terms of oz and oz using the chain rule Əz მყ • in terms of u using the expression of z(u) in the curve r2 (d) Deduce the partial derivative 32 and 33 at the point P and the equation of მე მყ the tangent plane

Chapter 3 Solutions

Calculus Combo

Ch. 3.1 - Prob. 9CCh. 3.1 - Prob. 10CCh. 3.1 - Prob. 11CCh. 3.1 - Prob. 12CCh. 3.1 - Prob. 13CCh. 3.1 - Prob. 14CCh. 3.1 - Prob. 15CCh. 3.1 - Prob. 16CCh. 3.1 - Prob. 17CCh. 3.1 - Prob. 18CCh. 3.1 - Prob. 19CCh. 3.1 - Prob. 20CCh. 3.1 - Prob. 21CCh. 3.1 - Prob. 22CCh. 3.1 - Prob. 23SCh. 3.1 - Prob. 24SCh. 3.1 - Prob. 25SCh. 3.1 - Prob. 26SCh. 3.1 - Prob. 27SCh. 3.1 - Prob. 28SCh. 3.1 - Prob. 29SCh. 3.1 - Prob. 30SCh. 3.1 - Prob. 31SCh. 3.1 - Prob. 32SCh. 3.1 - Prob. 33SCh. 3.1 - Prob. 34SCh. 3.1 - Prob. 35SCh. 3.1 - Prob. 36SCh. 3.1 - Prob. 37SCh. 3.1 - Prob. 38SCh. 3.1 - Prob. 39SCh. 3.1 - Prob. 40SCh. 3.1 - Prob. 41SCh. 3.1 - Prob. 42SCh. 3.1 - Prob. 43SCh. 3.1 - Prob. 44SCh. 3.1 - Prob. 45SCh. 3.1 - Prob. 46SCh. 3.1 - Prob. 47SCh. 3.1 - Prob. 48SCh. 3.1 - Prob. 49SCh. 3.1 - Prob. 50SCh. 3.1 - Prob. 51SCh. 3.1 - Prob. 52SCh. 3.1 - Prob. 53SCh. 3.1 - Prob. 54SCh. 3.1 - Prob. 55SCh. 3.1 - Prob. 56SCh. 3.1 - Prob. 57SCh. 3.1 - Prob. 58SCh. 3.1 - Prob. 59SCh. 3.1 - Prob. 60SCh. 3.1 - Prob. 61ACh. 3.1 - Prob. 62ACh. 3.1 - Prob. 63ACh. 3.1 - Prob. 64PCh. 3.1 - Prob. 65PCh. 3.1 - Prob. 66PCh. 3.1 - Prob. 67PCh. 3.1 - Prob. 68PCh. 3.1 - Prob. 69PCh. 3.1 - Prob. 1TFCh. 3.1 - Prob. 2TFCh. 3.1 - Prob. 3TFCh. 3.1 - Prob. 4TFCh. 3.1 - Prob. 5TFCh. 3.1 - Prob. 6TFCh. 3.1 - Prob. 7TFCh. 3.1 - Prob. 8TFCh. 3.2 - Prob. 1TBCh. 3.2 - Prob. 2TBCh. 3.2 - Prob. 3TBCh. 3.2 - Prob. 0CCh. 3.2 - Prob. 1CCh. 3.2 - Prob. 2CCh. 3.2 - Prob. 3CCh. 3.2 - Prob. 4CCh. 3.2 - Prob. 5CCh. 3.2 - Prob. 6CCh. 3.2 - Prob. 7CCh. 3.2 - Prob. 8CCh. 3.2 - Prob. 9CCh. 3.2 - Prob. 10CCh. 3.2 - Prob. 11CCh. 3.2 - Prob. 12CCh. 3.2 - Prob. 13CCh. 3.2 - Prob. 14CCh. 3.2 - Prob. 15CCh. 3.2 - Prob. 16CCh. 3.2 - Prob. 17CCh. 3.2 - Prob. 18CCh. 3.2 - Prob. 19SCh. 3.2 - Prob. 20SCh. 3.2 - Prob. 21SCh. 3.2 - Prob. 22SCh. 3.2 - Prob. 23SCh. 3.2 - Prob. 24SCh. 3.2 - Prob. 25SCh. 3.2 - Prob. 26SCh. 3.2 - Prob. 27SCh. 3.2 - Prob. 28SCh. 3.2 - Prob. 29SCh. 3.2 - Prob. 30SCh. 3.2 - Prob. 31SCh. 3.2 - Prob. 32SCh. 3.2 - Prob. 33SCh. 3.2 - Prob. 34SCh. 3.2 - Prob. 35SCh. 3.2 - Prob. 36SCh. 3.2 - Prob. 37SCh. 3.2 - Prob. 38SCh. 3.2 - Prob. 39SCh. 3.2 - Prob. 40SCh. 3.2 - Prob. 41SCh. 3.2 - Prob. 42SCh. 3.2 - Prob. 43SCh. 3.2 - Prob. 44SCh. 3.2 - Prob. 45SCh. 3.2 - Prob. 46SCh. 3.2 - Prob. 47SCh. 3.2 - Prob. 48SCh. 3.2 - Prob. 49SCh. 3.2 - Prob. 50SCh. 3.2 - Prob. 51SCh. 3.2 - Prob. 52SCh. 3.2 - Prob. 53SCh. 3.2 - Prob. 54SCh. 3.2 - Prob. 55SCh. 3.2 - Prob. 56SCh. 3.2 - Prob. 57SCh. 3.2 - Prob. 58SCh. 3.2 - Prob. 59SCh. 3.2 - Prob. 60SCh. 3.2 - Prob. 61SCh. 3.2 - Prob. 62SCh. 3.2 - Prob. 63SCh. 3.2 - Prob. 64SCh. 3.2 - Prob. 65SCh. 3.2 - Prob. 66SCh. 3.2 - Prob. 67SCh. 3.2 - Prob. 68SCh. 3.2 - Prob. 69SCh. 3.2 - Prob. 70SCh. 3.2 - Prob. 71SCh. 3.2 - Prob. 72SCh. 3.2 - Prob. 73SCh. 3.2 - Prob. 74SCh. 3.2 - Prob. 75SCh. 3.2 - Prob. 76SCh. 3.2 - Prob. 77SCh. 3.2 - Prob. 78SCh. 3.2 - Prob. 79SCh. 3.2 - Prob. 80SCh. 3.2 - Prob. 81SCh. 3.2 - Prob. 82SCh. 3.2 - Prob. 83ACh. 3.2 - Prob. 84ACh. 3.2 - Prob. 85ACh. 3.2 - Prob. 86ACh. 3.2 - Prob. 87PCh. 3.2 - Prob. 88PCh. 3.2 - Prob. 89PCh. 3.2 - Prob. 90PCh. 3.2 - Prob. 91PCh. 3.2 - Prob. 92PCh. 3.2 - Prob. 1TFCh. 3.2 - Prob. 2TFCh. 3.3 - Prob. 1TBCh. 3.3 - Prob. 2TBCh. 3.3 - Prob. 0CCh. 3.3 - Prob. 1CCh. 3.3 - Prob. 2CCh. 3.3 - Prob. 3CCh. 3.3 - Prob. 4CCh. 3.3 - Prob. 5CCh. 3.3 - Prob. 6CCh. 3.3 - Prob. 7CCh. 3.3 - Prob. 8CCh. 3.3 - Prob. 9CCh. 3.3 - Prob. 10CCh. 3.3 - Prob. 11CCh. 3.3 - Prob. 12CCh. 3.3 - Prob. 13CCh. 3.3 - Prob. 14CCh. 3.3 - Prob. 15CCh. 3.3 - Prob. 16CCh. 3.3 - Prob. 17CCh. 3.3 - Prob. 18CCh. 3.3 - Prob. 19CCh. 3.3 - Prob. 20CCh. 3.3 - Prob. 21SCh. 3.3 - Prob. 22SCh. 3.3 - Prob. 23SCh. 3.3 - Prob. 24SCh. 3.3 - Prob. 25SCh. 3.3 - Prob. 26SCh. 3.3 - Prob. 27SCh. 3.3 - Prob. 28SCh. 3.3 - Prob. 29SCh. 3.3 - Prob. 30SCh. 3.3 - Prob. 31SCh. 3.3 - Prob. 32SCh. 3.3 - Prob. 33SCh. 3.3 - Prob. 34SCh. 3.3 - Prob. 35SCh. 3.3 - Prob. 36SCh. 3.3 - Prob. 37SCh. 3.3 - Prob. 38SCh. 3.3 - Prob. 39SCh. 3.3 - Prob. 40SCh. 3.3 - Prob. 41SCh. 3.3 - Prob. 42SCh. 3.3 - Prob. 43SCh. 3.3 - Prob. 44SCh. 3.3 - Prob. 45SCh. 3.3 - Prob. 46SCh. 3.3 - Prob. 47SCh. 3.3 - Prob. 48SCh. 3.3 - Prob. 49SCh. 3.3 - Prob. 50SCh. 3.3 - Prob. 51SCh. 3.3 - Prob. 52SCh. 3.3 - Prob. 53SCh. 3.3 - Prob. 54SCh. 3.3 - Prob. 55SCh. 3.3 - Prob. 56SCh. 3.3 - Prob. 57SCh. 3.3 - Prob. 58SCh. 3.3 - Prob. 59SCh. 3.3 - Prob. 60SCh. 3.3 - Prob. 61SCh. 3.3 - Prob. 62SCh. 3.3 - Prob. 63SCh. 3.3 - Prob. 64SCh. 3.3 - Prob. 65SCh. 3.3 - Prob. 66SCh. 3.3 - Prob. 67SCh. 3.3 - Prob. 68SCh. 3.3 - Prob. 69SCh. 3.3 - Prob. 70SCh. 3.3 - Prob. 71SCh. 3.3 - Prob. 72SCh. 3.3 - Prob. 73SCh. 3.3 - Prob. 74SCh. 3.3 - Prob. 75SCh. 3.3 - Prob. 76SCh. 3.3 - Prob. 77SCh. 3.3 - Prob. 78SCh. 3.3 - Prob. 79SCh. 3.3 - Prob. 80SCh. 3.3 - Prob. 81SCh. 3.3 - Prob. 82SCh. 3.3 - Prob. 83SCh. 3.3 - Prob. 84SCh. 3.3 - Prob. 85SCh. 3.3 - Prob. 86SCh. 3.3 - Prob. 87ACh. 3.3 - Prob. 88ACh. 3.3 - Prob. 89ACh. 3.3 - Prob. 90ACh. 3.3 - Prob. 91PCh. 3.3 - Prob. 92PCh. 3.3 - Prob. 93PCh. 3.3 - Prob. 94PCh. 3.3 - Prob. 95PCh. 3.3 - Prob. 1TFCh. 3.3 - Prob. 2TFCh. 3.4 - Prob. 1TBCh. 3.4 - Prob. 2TBCh. 3.4 - Prob. 0CCh. 3.4 - Prob. 1CCh. 3.4 - Prob. 2CCh. 3.4 - Prob. 3CCh. 3.4 - Prob. 4CCh. 3.4 - Prob. 5CCh. 3.4 - Prob. 6CCh. 3.4 - Prob. 7CCh. 3.4 - Prob. 8CCh. 3.4 - Prob. 9CCh. 3.4 - Prob. 10CCh. 3.4 - Prob. 11SCh. 3.4 - Prob. 12SCh. 3.4 - Prob. 13SCh. 3.4 - Prob. 14SCh. 3.4 - Prob. 15SCh. 3.4 - Prob. 16SCh. 3.4 - Prob. 17SCh. 3.4 - Prob. 18SCh. 3.4 - Prob. 19SCh. 3.4 - Prob. 20SCh. 3.4 - Prob. 21SCh. 3.4 - Prob. 22SCh. 3.4 - Prob. 23SCh. 3.4 - Prob. 24SCh. 3.4 - Prob. 25SCh. 3.4 - Prob. 26SCh. 3.4 - Prob. 27SCh. 3.4 - Prob. 28SCh. 3.4 - Prob. 29SCh. 3.4 - Prob. 30SCh. 3.4 - Prob. 31SCh. 3.4 - Prob. 32SCh. 3.4 - Prob. 33SCh. 3.4 - Prob. 34SCh. 3.4 - Prob. 35ACh. 3.4 - Prob. 36ACh. 3.4 - Prob. 37ACh. 3.4 - Prob. 38ACh. 3.4 - Prob. 39ACh. 3.4 - Prob. 40ACh. 3.4 - Prob. 41ACh. 3.4 - Prob. 42ACh. 3.4 - Prob. 43ACh. 3.4 - Prob. 44ACh. 3.4 - Prob. 45ACh. 3.4 - Prob. 46ACh. 3.4 - Prob. 47ACh. 3.4 - Prob. 48ACh. 3.4 - Prob. 49ACh. 3.4 - Prob. 50ACh. 3.4 - Prob. 51ACh. 3.4 - Prob. 52ACh. 3.4 - Prob. 53ACh. 3.4 - Prob. 54ACh. 3.4 - Prob. 55ACh. 3.4 - Prob. 56ACh. 3.4 - Prob. 57ACh. 3.4 - Prob. 58ACh. 3.4 - Prob. 59ACh. 3.4 - Prob. 60ACh. 3.4 - Prob. 61ACh. 3.4 - Prob. 62ACh. 3.4 - Prob. 63PCh. 3.4 - Prob. 64PCh. 3.4 - Prob. 1TFCh. 3.4 - Prob. 2TFCh. 3.4 - Prob. 3TFCh. 3.4 - Prob. 4TFCh. 3.4 - Prob. 5TFCh. 3.5 - Prob. 1TBCh. 3.5 - Prob. 2TBCh. 3.5 - Prob. 0CCh. 3.5 - Prob. 1CCh. 3.5 - Prob. 2CCh. 3.5 - Prob. 3CCh. 3.5 - Prob. 4CCh. 3.5 - Prob. 5CCh. 3.5 - Prob. 6CCh. 3.5 - Prob. 7CCh. 3.5 - Prob. 8CCh. 3.5 - Prob. 9CCh. 3.5 - Prob. 10CCh. 3.5 - Prob. 11CCh. 3.5 - Prob. 12CCh. 3.5 - Prob. 13CCh. 3.5 - Prob. 14CCh. 3.5 - Prob. 15CCh. 3.5 - Prob. 16CCh. 3.5 - Prob. 17CCh. 3.5 - Prob. 18CCh. 3.5 - Prob. 19SCh. 3.5 - Prob. 20SCh. 3.5 - Prob. 21SCh. 3.5 - Prob. 22SCh. 3.5 - Prob. 23SCh. 3.5 - Prob. 24SCh. 3.5 - Prob. 25SCh. 3.5 - Prob. 26SCh. 3.5 - Prob. 27SCh. 3.5 - Prob. 28SCh. 3.5 - Prob. 29SCh. 3.5 - Prob. 30SCh. 3.5 - Prob. 31SCh. 3.5 - Prob. 32SCh. 3.5 - Prob. 33SCh. 3.5 - Prob. 34SCh. 3.5 - Prob. 35SCh. 3.5 - Prob. 36SCh. 3.5 - Prob. 37ACh. 3.5 - Prob. 38ACh. 3.5 - Prob. 39ACh. 3.5 - Prob. 40ACh. 3.5 - Prob. 41ACh. 3.5 - Prob. 42ACh. 3.5 - Prob. 43ACh. 3.5 - Prob. 44ACh. 3.5 - Prob. 45ACh. 3.5 - Prob. 46ACh. 3.5 - Prob. 47ACh. 3.5 - Prob. 48ACh. 3.5 - Prob. 49ACh. 3.5 - Prob. 50ACh. 3.5 - Prob. 51ACh. 3.5 - Prob. 52ACh. 3.5 - Prob. 53ACh. 3.5 - Prob. 54ACh. 3.5 - Prob. 55ACh. 3.5 - Prob. 56ACh. 3.5 - Prob. 57ACh. 3.5 - Prob. 58ACh. 3.5 - Prob. 59ACh. 3.5 - Prob. 60ACh. 3.5 - Prob. 61ACh. 3.5 - Prob. 62PCh. 3.5 - Prob. 63PCh. 3.5 - Prob. 64PCh. 3.5 - Prob. 65PCh. 3.5 - Prob. 1TFCh. 3.5 - Prob. 2TFCh. 3.5 - Prob. 3TFCh. 3.5 - Prob. 4TFCh. 3.6 - Prob. 1TBCh. 3.6 - Prob. 2TBCh. 3.6 - Prob. 0CCh. 3.6 - Prob. 1CCh. 3.6 - Prob. 2CCh. 3.6 - Prob. 3CCh. 3.6 - Prob. 4CCh. 3.6 - Prob. 5CCh. 3.6 - Prob. 6CCh. 3.6 - Prob. 7CCh. 3.6 - Prob. 8CCh. 3.6 - Prob. 9CCh. 3.6 - Prob. 10CCh. 3.6 - Prob. 11CCh. 3.6 - Prob. 12CCh. 3.6 - Prob. 13CCh. 3.6 - Prob. 14CCh. 3.6 - Prob. 15SCh. 3.6 - Prob. 16SCh. 3.6 - Prob. 17SCh. 3.6 - Prob. 18SCh. 3.6 - Prob. 19SCh. 3.6 - Prob. 20SCh. 3.6 - Prob. 21SCh. 3.6 - Prob. 22SCh. 3.6 - Prob. 23SCh. 3.6 - Prob. 24SCh. 3.6 - Prob. 25SCh. 3.6 - Prob. 26SCh. 3.6 - Prob. 27SCh. 3.6 - Prob. 28SCh. 3.6 - Prob. 29SCh. 3.6 - Prob. 30SCh. 3.6 - Prob. 31SCh. 3.6 - Prob. 32SCh. 3.6 - Prob. 33SCh. 3.6 - Prob. 34SCh. 3.6 - Prob. 35SCh. 3.6 - Prob. 36SCh. 3.6 - Prob. 37SCh. 3.6 - Prob. 38SCh. 3.6 - Prob. 39SCh. 3.6 - Prob. 40SCh. 3.6 - Prob. 41SCh. 3.6 - Prob. 42SCh. 3.6 - Prob. 43SCh. 3.6 - Prob. 44SCh. 3.6 - Prob. 45SCh. 3.6 - Prob. 46SCh. 3.6 - Prob. 47SCh. 3.6 - Prob. 48SCh. 3.6 - Prob. 49SCh. 3.6 - Prob. 50SCh. 3.6 - Prob. 51SCh. 3.6 - Prob. 52SCh. 3.6 - Prob. 53SCh. 3.6 - Prob. 54SCh. 3.6 - Prob. 55SCh. 3.6 - Prob. 56SCh. 3.6 - Prob. 57SCh. 3.6 - Prob. 58SCh. 3.6 - Prob. 59SCh. 3.6 - Prob. 60SCh. 3.6 - Prob. 61SCh. 3.6 - Prob. 62SCh. 3.6 - Prob. 63SCh. 3.6 - Prob. 64SCh. 3.6 - Prob. 65SCh. 3.6 - Prob. 66SCh. 3.6 - Prob. 67SCh. 3.6 - Prob. 68SCh. 3.6 - Prob. 69SCh. 3.6 - Prob. 70SCh. 3.6 - Prob. 71SCh. 3.6 - Prob. 72SCh. 3.6 - Prob. 73SCh. 3.6 - Prob. 74SCh. 3.6 - Prob. 75SCh. 3.6 - Prob. 76SCh. 3.6 - Prob. 77SCh. 3.6 - Prob. 78SCh. 3.6 - Prob. 79SCh. 3.6 - Prob. 80SCh. 3.6 - Prob. 81SCh. 3.6 - Prob. 82SCh. 3.6 - Prob. 83SCh. 3.6 - Prob. 84SCh. 3.6 - Prob. 85SCh. 3.6 - Prob. 86SCh. 3.6 - Prob. 87ACh. 3.6 - Prob. 88ACh. 3.6 - Prob. 89ACh. 3.6 - Prob. 90PCh. 3.6 - Prob. 91PCh. 3.6 - Prob. 92PCh. 3.6 - Prob. 93PCh. 3.6 - Prob. 94PCh. 3.6 - Prob. 95PCh. 3.6 - Prob. 1TFCh. 3.6 - Prob. 2TFCh. 3.6 - Prob. 3TFCh. 3.6 - Prob. 4TFCh. 3 - Prob. 1DCh. 3 - Prob. 2DCh. 3 - Prob. 3DCh. 3 - Prob. 4DCh. 3 - Prob. 5DCh. 3 - Prob. 6DCh. 3 - Prob. 1TCh. 3 - Prob. 2TCh. 3 - Prob. 3TCh. 3 - Prob. 4TCh. 3 - Prob. 5TCh. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Prob. 9TCh. 3 - Prob. 10TCh. 3 - Prob. 11TCh. 3 - Prob. 12TCh. 3 - Prob. 13TCh. 3 - Prob. 14TCh. 3 - Prob. 1GFTCh. 3 - Prob. 2GFTCh. 3 - Prob. 3GFTCh. 3 - Prob. 4GFTCh. 3 - Prob. 5GFTCh. 3 - Prob. 6GFTCh. 3 - Prob. 7GFTCh. 3 - Prob. 8GFTCh. 3 - Prob. 9GFTCh. 3 - Prob. 1SCCh. 3 - Prob. 2SCCh. 3 - Prob. 3SCCh. 3 - Prob. 4SCCh. 3 - Prob. 5SCCh. 3 - Prob. 6SCCh. 3 - Prob. 7SCCh. 3 - Prob. 8SCCh. 3 - Prob. 9SCCh. 3 - Prob. 10SCCh. 3 - Prob. 11SCCh. 3 - Prob. 12SCCh. 3 - Prob. 13SCCh. 3 - Prob. 14SCCh. 3 - Prob. 15SCCh. 3 - Prob. 16SCCh. 3 - Prob. 17SCCh. 3 - Prob. 18SCCh. 3 - Prob. 19SCCh. 3 - Prob. 20SCCh. 3 - Prob. 21SCCh. 3 - Prob. 22SCCh. 3 - Prob. 23SCCh. 3 - Prob. 24SCCh. 3 - Prob. 25SCCh. 3 - Prob. 26SCCh. 3 - Prob. 27SCCh. 3 - Prob. 28SCCh. 3 - Prob. 29SCCh. 3 - Prob. 30SCCh. 3 - Prob. 31SCCh. 3 - Prob. 32SCCh. 3 - Prob. ACPCh. 3 - Prob. BCPCh. 3 - Prob. CCPCh. 3 - Prob. DCP
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