Roboguru

Diketahui fungsi  maka hasil dari  adalah... .

Pertanyaan

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals 2 x squared plus 5 x end style maka hasil dari begin mathsize 14px style limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f left parenthesis x right parenthesis over denominator h end fraction end style adalah... .

Pembahasan Soal:

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals 2 x squared plus 5 x end style maka hasil dari begin mathsize 14px style limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction end style sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 open parentheses x plus h close parentheses squared plus 5 open parentheses x plus h close parentheses minus open parentheses 2 x squared plus 5 x close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 open parentheses x squared plus 2 x h plus h squared close parentheses plus 5 x plus 5 h minus 2 x squared minus 5 x over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 x squared plus 4 x h plus 2 h squared plus 5 x plus 5 h minus 2 x squared minus 5 x over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 x squared minus 2 x squared plus 5 x minus 5 x plus 2 h squared plus 4 x h plus 5 h over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 h squared plus 4 x h plus 5 h over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator h open parentheses 2 h plus 4 x plus 5 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of open parentheses 2 h plus 4 x plus 5 close parentheses end cell row blank equals cell 2 open parentheses 0 close parentheses plus 4 x plus 5 end cell row blank equals cell 4 x plus 5 end cell row blank blank blank end table end style


Jadi, begin mathsize 14px style limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction equals 4 x plus 5 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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