Show that Rn(x), the lagrange’s form of remainder in the Maclaurin series expansion of , e4s tends to zero as n fi ¥. Hence obtain the Maclaurin’s infinite expansion for e4s .
To show that \( R_n(x) \), the Lagrange form of the remainder in the Maclaurin series expansion of \( e^{4x} \), tends to zero as \( n \) approaches infinity, we can use Taylor's Remainder Theorem. The Lagrange form of the remainder is given by:
\[ R_n(x) = \frac{f^{(n+1)}(c) x^{n+1}}{(n+1)!} \]
where \( c
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