Find the Taylor Series at X = 0 of the Function

question 63

Multiple Choice

Find the Taylor series at x = 0 of the function f(x) = x ln(1 + 2x) by computing three or four derivatives and using the definition of the Taylor series.

• A) 2 \(x ^ { 2 }\) - \(\frac { 4 x ^ { 3 } } { 2 }\)
• B) 2 \(x ^ { 2 }\) - \(\frac { 4 x ^ { 3 } } { 3 }\)
• C) \(2 x ^ { 2 }\) + \(\frac { 4 x ^ { 3 } } { 2 ! }\)
• D) 2x - \(\frac { 4 x ^ { 2 } } { 2 ! }\) + \(\frac { 8 x ^ { 3 } } { 3 ! }\)
• E) none of these