Question
Show that , the lagrange's form of remainder in the Maclaurin series expansion of e4x, tends to zero as
. Hence obtain the Maclaurin's infinite expansion for e4x.
Answer :
Word Count : 130
For the function (f(x) = e^{4x}), the Maclaurin series expansion is [ f(x) = f(0) + f'(0)x + \frac{f''(0)}{2!}x^2 + \dots + \frac{f^{(n)}(0)}{n!}x^n + R_n(x), ] where (R_n(x)) is the Lagrange form ______ ________ ________ _________ _______ _________ __________ ______.
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______ ________ ____.
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For the function (f(x) = e^{4x}), the Maclaurin series expansion is [ f(x) = f(0) + f'(0)x + \frac{f''(0)}{2!}x^2 + \dots + \frac{f^{(n)}(0)}{n!}x^n + R_n(x), ] where (R_n(x)) is the Lagrange form ______ ________ ________ _________ _______ _________ __________ ______.
________ ______ ________ _____ ________ ___ _________ _______ ________ ______.
________ __________ _______ ____ ________ ___ ___ ___ ________.
__________ _____ _______ _____ _________ _____.
____ ____ ____ ____ _________ ________ ________ __________ _______ _________.
__________ ________ __________ __________ _______ _______ ________ _______.
_______ __________ _____ ____ ____ ________ ____ ______ ______ ___ ___.
____ ________ __________ ________ __________ ____ _______ __________ _________.
________ __________ _____ ______ ______ ___ ______ _________ _____ _________ _____ __________.
________ _____ _________ ___ ________ ________ ___ ____ ________ __________ _______ ____.
______ ________ ____.
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