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Let f be a function in C (R), infinitesimal as x + 0 and with a minimum point at x =0. Then necessarily %3D O (A)f(x) = h+ kx² + o(x²), h, k E (0, +0) O (B) f(x) = kx² + o(x²), ke (0, +o0) O (C)f(x) = kx* + o(x*), kE (0, +o0) O (D) f'(0) = 0, and f'(x) 20 %3D %3D O (E) the smallest order of the derivative that is non-zero at x = O is even

Let f be a function in C (R), infinitesimal as x + 0 and with a minimum point at x =0. Then necessarily %3D O (A)f(x) = h+ kx² + o(x²), h, k E (0, +0) O (B) f(x) = kx² + o(x²), ke (0, +o0) O (C)f(x) = kx* + o(x*), kE (0, +o0) O (D) f'(0) = 0, and f'(x) 20 %3D %3D O (E) the smallest order of the derivative that is non-zero at x = O is even

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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Let f be a function in C (R), infinitesimal as x + 0 and with a minimum point at x = 0 Then necessarily %3D O (A) f(x) = h+ kx? + o(x²), h, k E (0, +0) O (B) f(x) = kx² + o(x²), k e (0, +o0) O (C)f(x) = kx* + o(x*), k E (0,+o0) O (D)f'(0) = 0, and f'(x) >0 %3D %3D %3D O (E) the smallest order of the derivative that is non-zero at x %3D O is even
Transcribed Image Text:Let f be a function in C (R), infinitesimal as x + 0 and with a minimum point at x = 0 Then necessarily %3D O (A) f(x) = h+ kx? + o(x²), h, k E (0, +0) O (B) f(x) = kx² + o(x²), k e (0, +o0) O (C)f(x) = kx* + o(x*), k E (0,+o0) O (D)f'(0) = 0, and f'(x) >0 %3D %3D %3D O (E) the smallest order of the derivative that is non-zero at x %3D O is even
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