Finding taylor series using the definition.

Problem

Let space, g, left parenthesis, x, right parenthesis, equals, e, start superscript, 2, x, plus, 2, end superscript, space and let space, T, start subscript, 3, end subscript, left parenthesis, x, right parenthesis, space be the third-degree Taylor polynomial for space, g, space centered at space, x, equals, 0, space. The sum of the coefficients of space, T, start subscript, 3, end subscript, space can be written as space, a, e, start superscript, 2, end superscript. Determine space, a, space.
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4