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Suppose that g: I→ R is differentiable at x = zo. Does the following limit g(ro+6h)-g(ro-6h) 12h exist? (Either prove your answer or give a counterexample). lim h→0 Is the converse true? That is suppose the limit lim h→0 g(xo +6h) - g(xo - 6h) 12h = L exists, is g differentiable at x = ro? (Either prove your answer or give a coun- terexample).

Suppose that g: I→ R is differentiable at x = zo. Does the following limit g(ro+6h)-g(ro-6h) 12h exist? (Either prove your answer or give a counterexample). lim h→0 Is the converse true? That is suppose the limit lim h→0 g(xo +6h) - g(xo - 6h) 12h = L exists, is g differentiable at x = ro? (Either prove your answer or give a coun- terexample).

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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Please can you help with this proof, many thanks.

Suppose that g: I→ R is differentiable at x =ro. Does the following limit g(ro +6h)-g(ro-6h) 12h exist? (Either prove your answer or give a counterexample). lim h→0 Is the converse true? That is suppose the limit lim h→0 g(xo +6h) - g(xo - 6h) 12h = L exists, is g differentiable at r = ro? (Either prove your answer or give a coun- terexample).
Transcribed Image Text:Suppose that g: I→ R is differentiable at x =ro. Does the following limit g(ro +6h)-g(ro-6h) 12h exist? (Either prove your answer or give a counterexample). lim h→0 Is the converse true? That is suppose the limit lim h→0 g(xo +6h) - g(xo - 6h) 12h = L exists, is g differentiable at r = ro? (Either prove your answer or give a coun- terexample).
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