Consider the following statement: if f and g are two infinitesimal functions of order 5 as x → x₀ with respect to the sample x - x₀, then the function f - g is an infinitesimal of order 5 as x → x₀ with respect to the sample x - x₀. Establish whether the statement is true or false, providing a justification for the answer.

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09-07-2024
Mathematics

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Consider the following statement: if f and g are two infinitesimal functions of order 5 as x → x₀ with respect to the sample x - x₀, then the function f - g is an infinitesimal of order 5 as x → x₀ with respect to the sample x - x₀. Establish whether the statement is true or false, providing a justification for the answer.

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