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. Let s (0, ∞) → R be the usual square root defined on the nonnegative reals: s(x) is the unique nonnegative real number t such that t² = x. (a) Give an expression for the derivative s(k) (1) = in the complex variable z. for an arbitrary k € N. You may use knowledge from previous courses in real calculus. (b) Compute the radius of convergence of the series ds(x) dak k=0 s(k) (1) ak k!

. Let s (0, ∞) → R be the usual square root defined on the nonnegative reals: s(x) is the unique nonnegative real number t such that t² = x. (a) Give an expression for the derivative s(k) (1) = in the complex variable z. for an arbitrary k € N. You may use knowledge from previous courses in real calculus. (b) Compute the radius of convergence of the series ds(x) dak k=0 s(k) (1) ak k!

Advanced Engineering Mathematics
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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2. Let s (0, ∞) → R be the usual square root defined on the nonnegative reals: s(x) is the unique nonnegative real number t such that t² = x. (a) Give an expression for the derivative s(k) (1) = in the complex variable z. dk drk k=0 s(x) for an arbitrary ke N. You may use knowledge from previous courses in real calculus. (b) Compute the radius of convergence of the series x=1 s(k) (1) z k k!
Transcribed Image Text:2. Let s (0, ∞) → R be the usual square root defined on the nonnegative reals: s(x) is the unique nonnegative real number t such that t² = x. (a) Give an expression for the derivative s(k) (1) = in the complex variable z. dk drk k=0 s(x) for an arbitrary ke N. You may use knowledge from previous courses in real calculus. (b) Compute the radius of convergence of the series x=1 s(k) (1) z k k!
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