Answered: Let f(x) -a)" be a convergent series…

Let f(x) -a)" be a convergent series n=0 where a- R< I0 and R > 0. Which of the following statements must be true for the function h(r, y) = >an cos y (r – a)" on the n=0 domain D = {(r, y) : a-R

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let f(r)
> an (x - a)" be a convergent series
n=0
where a - R <I<a+R for a > 0 and R> 0.
Which of the following statements must be true
for the function h(r, y) = >
an cos y (r- a)" on the
n=0
domain D = {(r, y): a-R<I<a+R,0< y< 27}?
I. h,(r, y) = sin y f(r).
II. h has continuous partial derivative with respect
to r at the point P ( + R,0).
III. h. has continuous partial derivative with respect
R
to r at the point Q (a+
2
IV. The point T (2a, )i
is a critical point of h(r, y).
I, IV
I only
II, III
I, II
П, IV

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