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Pertanyaan

Misalkan f ( x ) = x 2 + 3 x − 1 , hitunglah h → 0 lim ​ h f ( x + h ) − f ( h ) ​

Misalkan , hitunglah

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S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

dari fungsi adalah .

 limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis h right parenthesis over denominator h end fraction dari fungsi f left parenthesis x right parenthesis equals x squared plus 3 x minus 1 adalah 2 x plus 3.

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Pembahasan

Turunan dari fungsi dilambangkan dengan didefinisikan sebagai : Sehingga diperoleh, Jadi, dari fungsi adalah .

Turunan dari fungsi f left parenthesis x right parenthesis dilambangkan dengan f apostrophe left parenthesis x right parenthesisdidefinisikan sebagai :

limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis h right parenthesis over denominator h end fraction

Sehingga diperoleh,

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis h right parenthesis over denominator h end fraction end cell equals cell limit as h rightwards arrow 0 of fraction numerator left parenthesis x plus h right parenthesis squared plus 3 left parenthesis x plus h right parenthesis minus 1 minus open parentheses x squared plus 3 x minus 1 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator x squared plus 2 x h plus h squared plus 3 x plus 3 h minus 1 minus x squared minus 3 x plus 1 over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 x h plus 3 h plus h squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator up diagonal strike h left parenthesis 2 x plus 3 plus h right parenthesis over denominator up diagonal strike h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space 2 x plus 3 plus h end cell row blank equals cell 2 x plus 3 plus 0 end cell row blank equals cell 2 x plus 3 end cell end table

Jadi, limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis h right parenthesis over denominator h end fraction dari fungsi f left parenthesis x right parenthesis equals x squared plus 3 x minus 1 adalah 2 x plus 3.

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