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Find the First Four Non-Zero Terms of the Taylor Series f(x)=sin⁡2xf ( x ) = \sin 2 x

Question 108

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Find the first four non-zero terms of the Taylor series at x = 0 of f(x)=sin⁡2xf ( x ) = \sin 2 x .
Is f(x)=2x−8x33!+32x55!−128x77!f ( x ) = 2 x - \frac { 8 x ^ { 3 } } { 3 ! } + \frac { 32 x ^ { 5 } } { 5 ! } - \frac { 128 x ^ { 7 } } { 7 ! } the correct answer?

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