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Exercise 6.6.6. Review the proof that g'(0) = 0 for the function 9(x) = { 0-1 e-1/x2 for x 0, for x = 0. aid T introduced at the end of this section. (a) Compute g'(x) for x 0. Then use the definition of the derivative to find g"(0). (b) Compute g"(x) and g'(x) for x 0. Use these observations and in- vent whatever notation is needed to give a general description for the nth derivative g(n) (x) at points different from zero. (c) Construct a general argument for why g(n) (0) = 0 for all nЄ N.

Exercise 6.6.6. Review the proof that g'(0) = 0 for the function 9(x) = { 0-1 e-1/x2 for x 0, for x = 0. aid T introduced at the end of this section. (a) Compute g'(x) for x 0. Then use the definition of the derivative to find g"(0). (b) Compute g"(x) and g'(x) for x 0. Use these observations and in- vent whatever notation is needed to give a general description for the nth derivative g(n) (x) at points different from zero. (c) Construct a general argument for why g(n) (0) = 0 for all nЄ N.

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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Exercise 6.6.6. Review the proof that g'(0) = 0 for the function 9(x) = { 0-1 e-1/x2 for x 0, for x = 0. aid T introduced at the end of this section. (a) Compute g'(x) for x 0. Then use the definition of the derivative to find g"(0). (b) Compute g"(x) and g'(x) for x 0. Use these observations and in- vent whatever notation is needed to give a general description for the nth derivative g(n) (x) at points different from zero. (c) Construct a general argument for why g(n) (0) = 0 for all nЄ N.
Transcribed Image Text:Exercise 6.6.6. Review the proof that g'(0) = 0 for the function 9(x) = { 0-1 e-1/x2 for x 0, for x = 0. aid T introduced at the end of this section. (a) Compute g'(x) for x 0. Then use the definition of the derivative to find g"(0). (b) Compute g"(x) and g'(x) for x 0. Use these observations and in- vent whatever notation is needed to give a general description for the nth derivative g(n) (x) at points different from zero. (c) Construct a general argument for why g(n) (0) = 0 for all nЄ N.
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