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(Solved): clear steps 4- (a) Using the series expansions of \( \cos (x) \) and \( \sin (x) \) prove Euler's id ...
clear steps
4- (a) Using the series expansions of \( \cos (x) \) and \( \sin (x) \) prove Euler's identities i. \( e^{k x}=\cos (x)+i \sin (x) \) ii. \( e^{-i x}=\cos (x)= \) isin \( (x) \) (b) Find the series expansion of \( \exp \left(-x^{3}\right) \).