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Get Full Access to Calculus: Early Transcendentals - 2 Edition - Chapter 13.5 - Problem 31
Get Full Access to Calculus: Early Transcendentals - 2 Edition - Chapter 13.5 - Problem 31

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# Solved: 2934. Volumes in cylindrical coordinates Use cylindrical coordinates to find the

ISBN: 9780321947345 167

## Solution for problem 31 Chapter 13.5

Calculus: Early Transcendentals | 2nd Edition

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Problem 31

2934. Volumes in cylindrical coordinates Use cylindrical coordinates to find the volume of the following solids. The solid bounded by the plane z = 129 and the hyperboloid z = 24 + x2 + y2 z x y z _ 4 _ x2 _ y2 29

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Overview week of 9/12/16 3.3 Rules of Differentiation Power of X: d n (n­1) Power Rule: / Xdx= nX Quotient Rule: / f(x)/g(x) = [(f(x) * g(x)) – (f(x) * g(x))] / [g(x)] 2 dx Product Rule: / [dxx) * g(x)] = [f(x) * g’(x)] + [g(x) * f’(x)] Chain Rule: / [dxg(x))] = [f(g(x))]’ * g’(x) Constant Multiple: Power rule d /dx(cf(x)) = c * f ’(x) 3.4 Product and Quotient Rules Product Rule: While [f(x) +/­ g(x)]’ = f ‘(x) +/­ g’(x), The same does not apply to multiplication And division. [f(x)g(x)] ≠ f ‘(x) * g’(x) Instead: [f(x)g(x)] = [f(x) * g’(x)] + [g(x) * f’(x)] Products of multiple functions: (fg)’ = f’g + fg’ (fgh)’ = f’gh + fg’h + fgh’ (fghi)’ = f’ghi + fg’hi + fgh’i + fghi’

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