No cálculo de limites, muitas vezes nos deparamos com situações as quais os limites são indeterminados. Nestes casos, utiliza-se a Regra de L’Hôpital. Seu objetivo é calcular o limite de frações quando há indeterminações. Sejam f e g funções contínuas e deriváveis em um intervalo ou união de intervalos I, com g apostrophe space left parenthesis x right parenthesis not equal to 0 comma for all space x element of I. Sestack l i m with x rightwards arrow a below space f left parenthesis x right parenthesis to the power of blank space equals stack l i m with x rightwards arrow a below space g left parenthesis x right parenthesis equals 0 space o u space stack l i m with x rightwards arrow a below f left parenthesis x right parenthesis equals stack l i m with x rightwards arrow a below g left parenthesis x right parenthesis equals infinity E se existe stack l i m with x rightwards arrow a below fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction finito ou infinito, então: stack l i m with x rightwards arrow a below begin inline style fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction end style begin inline style equals end style begin inline style stack l i m with x rightwards arrow a below end style begin inline style fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe space left parenthesis x right parenthesis end fraction end style begin inline style space end style begin inline style p end style begin inline style a end style begin inline style r end style begin inline style a end style begin inline style space end style begin inline style a end style begin inline style equals end style begin inline style begin inline style a end style to the power of plus end style begin inline style o end style begin inline style u end style begin inline style space end style begin inline style begin inline style a end style to the power of minus end style begin inline style space end style begin inline style o end style begin inline style u end style begin inline style space end style begin inline style infinity end style begin inline style space end style begin inline style o end style begin inline style u end style begin inline style space end style begin inline style minus end style begin inline style infinity end style begin inline style. end style Com base nestas informações, determine stack l i m with left parenthesis x rightwards arrow 0 right parenthesis below open parentheses begin inline style fraction numerator e to the power of 4 x minus 1 end exponent over denominator 2 x end fraction end style space close parentheses space, através da aplicação da regra de L'Hôpital.
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Desculpe mas isso está um pouco baralhado
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ageita ai que eu te respondo
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