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Berat (dalam gram) dari suatu benda uji pada saat  adalah  ( diukur dalam minggu). Berapa laju pertambahan berat benda uji jika  minggu?

Pertanyaan

Berat (dalam gram) dari suatu benda uji pada saat undefined adalah begin mathsize 14px style w left parenthesis t right parenthesis equals 0 comma 1 t squared minus 0 comma 05 t end style (undefined diukur dalam minggu). Berapa laju pertambahan berat benda uji jika begin mathsize 14px style t equals 10 end style minggu?

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Pembahasan Video:

Pembahasan Soal:

begin mathsize 14px style w left parenthesis t right parenthesis equals 0 comma 1 t squared minus 0 comma 05 t end style

Laju pertambahan berat benda uji jika begin mathsize 14px style t equals 10 end style minggu adalah:

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 left parenthesis t plus h right parenthesis minus f left parenthesis t right parenthesis over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator left square bracket 0 comma 1 times left parenthesis t plus h right parenthesis squared minus 0 comma 05 times left parenthesis t plus h right parenthesis right square bracket minus left square bracket 0 comma 1 times t squared minus 0 comma 05 times t right square bracket over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator left square bracket 0 comma 1 times left parenthesis 10 plus h right parenthesis squared minus 0 comma 05 times left parenthesis 10 plus h right parenthesis right square bracket minus left square bracket 0 comma 1 times 10 squared minus 0 comma 05 times 10 right square bracket over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator left square bracket 0 comma 1 times left parenthesis 100 plus 20 h plus h squared right parenthesis minus 0 comma 5 minus 0 comma 05 h right square bracket minus 10 plus 0 comma 5 over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 0 comma 1 h squared plus 2 h plus 10 minus 0 comma 5 minus 0 comma 05 h minus 10 plus 0 comma 5 over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 0 comma 1 h squared plus 1 comma 95 h over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of left parenthesis 0 comma 1 h plus 1 comma 95 right parenthesis end cell row blank equals cell 0 comma 1 times left parenthesis 0 right parenthesis plus 1 comma 95 end cell row blank equals cell 1 comma 95 end cell end table end style 

Jadi, pertambahan berat benda uji tersebut adalah begin mathsize 14px style 1 comma 95 space gram divided by minggu end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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