Chamamos de transformada de Laplace a expressão script capital l open curly brackets f left parenthesis t right parenthesis close curly brackets equals integral subscript 0 superscript infinity e to the power of negative s t end exponent f left parenthesis t right parenthesis d t comma space com t greater or equal than 0 Observe as funções e transformadas a seguir: 1. f left parenthesis t right parenthesis equals e to the power of negative 3 t end exponent i. script capital l open curly brackets f left parenthesis t right parenthesis close curly brackets equals fraction numerator negative 7 s squared plus 12 over denominator s squared left parenthesis s squared plus 4 right parenthesis end fraction 2. f left parenthesis t right parenthesis equals 3 t minus 5 sin left parenthesis 2 t right parenthesis ii. script capital l open curly brackets f left parenthesis t right parenthesis close curly brackets equals fraction numerator 2 over denominator s left parenthesis s squared plus 4 right parenthesis end fraction 3. f left parenthesis t right parenthesis equals t e to the power of negative 2 t end exponent iii. script capital l open curly brackets f left parenthesis t right parenthesis close curly brackets equals 1 over left parenthesis s plus 2 right parenthesis squared 4. f left parenthesis t right parenthesis equals sin squared left parenthesis t right parenthesis iv. script capital l open curly brackets f left parenthesis t right parenthesis close curly brackets equals fraction numerator 1 over denominator left parenthesis s plus 3 right parenthesis end fraction Baseado nas informações do texto-base e nos conteúdos da unidade, assinale a alternativa que apresenta a relação correta entre a função e sua transformada. Alternativas: a) 1.iv; 2.i; 3.iii; 4.ii b) 1.iv; 2.iii; 3.ii; 4.i c) 1.ii; 2.i; 3.iv; 4.iii d) 1.iii; 2.ii; 3.iv; 4.i e) 1.i; 2.iv; 3.ii; 4.iii