... x =2andwhenx=−2, the second converges when x = −2, and diverges when x = 2, while the third converges both when x =2andwhenx=−2.These results are all easy to check by direct substitution, and ... section of the right hand half of the solid outside a cylinder of radiusa and inside the sphere of radius 2a 9972 CHAPTER 7. POWER SERIESProof. We can differentiate n times by 7.9 and we still get ... particle may depend on the position x and the time t,sowehavey=f(x, t);the volume V of a cylinder depends on the radius r of the base and its height h ,and indeed, as you know, V = πr2h; or...