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The Riemann zeta function, defined as ζ(s) = X∞ n = 11/ns is an extremely important function in mathematics (particularly number theory) and physics (string theory). While it has many applications, one of its primary uses is to estimate a distribution of prime numbers. It is the center of one of the greatest still-open problems in mathematics, called the Riemann Hypothesis (whose proof as true would be a giant boon to science).
(a) Determine if ζ(1) converges or diverges.
Set up different integrals to find the mass of the solid bounded by the equations z=8-2x, z=0, y=0, y=3 and x=0. the density of the solid at (x,y,z) is d(x,y,z)=kx, k>0. evaluate ONE of the integrals.
Find the critical points of the function and determine whether the critical point is a local minimum or maximum or neither. Enter your answers as a comma-separated list.
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