The First Four Nonzero Terms in the Power Series Expansion $f ( x ) = \sin x$

question 37

Multiple Choice

The first four nonzero terms in the power series expansion of the function $f ( x ) = \sin x$ about $x = 0$ are

• A) \(1 - x + x ^ { 2 } / 2 - x ^ { 3 } / 3\)
• B) \(x - x ^ { 3 } / 6 + x ^ { 5 } / 120 - x ^ { 7 } / 5040\)
• C) \(x + x ^ { 3 } + x ^ { 5 } + x ^ { 7 }\)
• D) \(1 + x ^ { 2 } / 2 + x ^ { 4 } / 4 + x ^ { 6 } / 6\)
• E) \(1 - x ^ { 2 } / 2 + x ^ { 4 } / 24 - x ^ { 6 } / 720\)