Use cylindrical coordinates to find the volume of the region bounded by the plane z = 0 and the hyperboloid z = √65-√1 + x² + y². Set up the triple integral using cylindrical coordinates that should be used to find the volume of the region as efficiently as possible. Use i 000 SSS Odz dr de 00 0

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Q: 3. Evaluate the following integral. Show complete solution. rtoo Sta e drdy (شرعی)

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A: We will find line integral by using stokes theorem .

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Q: 1. Define f(x) = & Prove that f: R→ R is continuous. if z 20 -2² if r ≤0

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Q: 3Q. Find a series solution around xo = 0 for the following differential equation. y" - 4y = 0

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Q: (a pour) = (d(1) a) +...+ d& T dG T dl) +04+ mos ad ppo desta sedang

A: Here we use that (p-i)^p=-(i^p) in mod p. We proof this by binomial expansion.

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Q: Suppose p is an odd prime. Show that (1² +2 +3P +...+ (p − 1)²) = 0 (mod p).

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