(b) Taking as given the fact limoe-1/* = 0 for all n € N, prove that for any polynomial function q(x) q(x)e-1/2 = 0 n explaining the use of limit laws and the given assumption. (Don't do an e-d proof.) lim 2-0 (c) Explain why this can be used to show that 7(0) = 0, for ğ: R→ R given by {a(z) (g(x) x>0 x≤ 0. g(x)= =
(b) Taking as given the fact limoe-1/* = 0 for all n € N, prove that for any polynomial function q(x) q(x)e-1/2 = 0 n explaining the use of limit laws and the given assumption. (Don't do an e-d proof.) lim 2-0 (c) Explain why this can be used to show that 7(0) = 0, for ğ: R→ R given by {a(z) (g(x) x>0 x≤ 0. g(x)= =
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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Solve all parts
Transcribed Image Text:(b) Taking as given the fact limoe-1/* = 0 for all n € N, prove that for any
polynomial function q(x)
q(x)e-1/2
= 0
lim
2-0 2n
explaining the use of limit laws and the given assumption. (Don't do an e-d
proof.)
(c) Explain why this can be used to show that g'(0) = 0, for ğ: R→ R given by
{a(z)
(g(x) x>0
x≤ 0.
g(x)=
=
Transcribed Image Text:The following question deals with my favourite function.
(a) Prove that for all k € N, and for an arbitrary polynomial function p(x), the
derivative of the function g: (0, ∞) → R given by
g(x) = P(x)e-1/x
xk
is again a function of the same form.
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