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Carilah nilai f(x) jika f (x)=x​+x​2​ dan f(1)=1

Pertanyaan

Carilah nilai undefined jika begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals square root of x plus fraction numerator 2 over denominator square root of x end fraction end style dan begin mathsize 14px style f left parenthesis 1 right parenthesis equals 1 end style 

  1. ...undefined 

  2. ...undefined 

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

f open parentheses x close parentheses equals blank integral f to the power of apostrophe open parentheses x close parentheses blank d x

f left parenthesis x right parenthesis equals integral open parentheses square root of x plus fraction numerator 2 over denominator square root of x blank end root end fraction close parentheses blank d x

f left parenthesis x right parenthesis space equals integral square root of x blank d x plus blank integral fraction numerator 2 over denominator square root of x blank end root end fraction d x

f left parenthesis x right parenthesis space equals space integral x to the power of 1 half end exponent blank d x plus integral 2 blank x to the power of negative 1 half end exponent blank d x blank

f open parentheses x close parentheses equals fraction numerator 1 over denominator 1 half plus 1 end fraction blank x to the power of 1 half plus 1 end exponent plus c plus fraction numerator 2 over denominator negative 1 half plus 1 end fraction blank x to the power of negative 1 half plus 1 end exponent plus c

f left parenthesis x right parenthesis space equals space fraction numerator 1 over denominator 3 over 2 end fraction x to the power of 3 over 2 end exponent plus fraction numerator 2 over denominator 1 half end fraction x to the power of 1 half end exponent plus C

f left parenthesis x right parenthesis space equals space 2 over 3 x to the power of 3 over 2 end exponent plus 4 blank x to the power of 1 half end exponent plus C

f left parenthesis x right parenthesis space equals space 2 over 3 x square root of x plus 4 square root of x plus C

Karena f left parenthesis 1 right parenthesis space equals 1, maka

f open parentheses 1 close parentheses equals 2 over 3 open parentheses 1 close parentheses blank square root of 1 plus 4 square root of 1 plus C

1 equals 2 over 3 plus 4 plus C

3 over 3 minus 2 over 3 minus 12 over 3 equals C

negative 11 over 3 equals C

Sehingga

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109

4.7 (8 rating)

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