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(Solved): Prove that 4ex is equal to the sum of its Maclaurin series. Solution If f(x)=4ex, then f(n+1)(x)= f ...




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Prove that is equal to the sum of its Maclaurin series. Solution If , then for all . If is any positive number and So Taylor's Inequality, with and , says that Notice that the same constant works for every value of . But, from this equation, we have It follows from the Squeeze Theorem that and therefore for ail values of . By this theorem, Ae is equal to the sum of its Maclaurin series, that is,


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