Question No. 6Suppose a and c are real numbers, c > 0 and f is defined on [-1,1] byfx" sin(lx|-)toif x + 0)if x = 0ff(x) =Prove thati.f is continuous if an only if a > 0.ii.f' is bounded if and only if a 2 1+ c.ii.f"(0)exists if and only if a > 2 + c.Vour answer

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Suppose a and c are real numbers, c > 0 and f is defined on -1,1] by fxª sin(]x|=) to if x # 0) if x = 05 f(x) = Prove that i. f is continuous if an only if a > 0. f' is bounded if and only if a 2 1+c. ii. ii. f"(0)exists if and only if a > 2 + c.

Suppose a and c are real numbers, c > 0 and f is defined on -1,1] by fxª sin(]x|=) to if x # 0) if x = 05 f(x) = Prove that i. f is continuous if an only if a > 0. f' is bounded if and only if a 2 1+c. ii. ii. f"(0)exists if and only if a > 2 + c.

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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