4. (a) Suppose that a function f satisfies |f (x)| < |x| for all x. Show that f is continuous at 0.(b) Suppose that a function g is continuous at 0 and satisfies g(0) = 0. Suppose furthermore thath is a function which satisfies |h(x)| < |g(x)| for all x. Show that h is continuous at 0.

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Answered: 4. (a) Suppose that a function f…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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4. (a) Suppose that a function f satisfies |f (x)| < |x| for all x. Show that f is continuous at 0. (b) Suppose that a function g is continuous at 0 and satisfies g(0) = 0. Suppose furthermore that h is a function which satisfies |h(x)| < |g(x)| for all x. Show that h is continuous at 0. %3D