Question

É uma serie de funções cujos são obtidos multiplicando-se os senos e os cossenos dos múltiplos sucessivos da Variável independente x por coeficiente, que não dependem

da variável x e são admitidos reais. 1 half a subscript 0 plus space a subscript 1 space cos space x space plus space space a subscript 2 space end subscript cos space 2 x space plus... space space plus space b subscript 1 space s e n space x space plus space b subscript 2 space s e n space 2 x space plus... ou



space a subscript 0 over 2 plus space sum from k equals 1 to infinity of left parenthesis straight a subscript straight n space cos left parenthesis n x right parenthesis space plus space straight b subscript straight n space sen space left parenthesis n x right parenthesis right parenthesis

Neste contexto, determine o desenvolvimento em série de Fourier da seguinte função:



f left parenthesis x right parenthesis space equals space x space plus space 1 space p a r a space x space element of left square bracket negative 1 comma space 1 right square bracket





Agora, assinale a alternativa correta.
Escolha uma:
a.

straight f left parenthesis straight x right parenthesis space equals space 2 over 2 plus sum from straight k equals 1 to infinity of fraction numerator left parenthesis negative 1 right parenthesis to the power of straight k plus 1 end exponent over denominator 2 kπ end fraction sen left parenthesis kπx right parenthesis.
b.

straight f left parenthesis straight x right parenthesis space equals space 1 half plus sum from straight k equals 1 to infinity of 2 over kπ sen left parenthesis kπx right parenthesis.
c.

straight f left parenthesis straight x right parenthesis space equals space 2 over 2 plus sum from straight k equals 1 to infinity of fraction numerator left parenthesis negative 1 right parenthesis to the power of straight k plus 1 end exponent over denominator kπ end fraction sen left parenthesis kπx right parenthesis.
d.

straight f left parenthesis straight x right parenthesis space equals space 2 over 2 plus sum from straight k equals 1 to infinity of fraction numerator 2 left parenthesis negative 1 right parenthesis to the power of straight k plus 1 end exponent over denominator kπ end fraction sen left parenthesis kπx right parenthesis.
e.

straight f left parenthesis straight x right parenthesis space equals space sum from straight k equals 1 to infinity of fraction numerator 2 left parenthesis negative 1 right parenthesis to the power of straight k plus 1 end exponent over denominator kπ end fraction sen left parenthesis kπx right parenthesis.

Answer 1

Resposta correta é a D