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Sehuah halon berbentuk bola. Balon tersebut dipompa sehingga volume udara dalam balon meningkat. Laju penambahan volume bola cm3/detik untuk waktu mendekati nilai tertentu dapat ditentukan menggunakan rumus t→t1​lim​t−t1​V(t)−V(t1​)​. Jika V(t)=3,6×10−5πt3, berapakah laju penambahan volume bola pada waktu mendekati 10 detik setelah dipompa?

Pertanyaan

Sehuah halon berbentuk bola. Balon tersebut dipompa sehingga volume udara dalam balon meningkat. Laju penambahan volume bola begin mathsize 14px style cm cubed divided by detik end style untuk waktu mendekati nilai tertentu dapat ditentukan menggunakan rumus begin mathsize 14px style limit as t rightwards arrow t subscript 1 of fraction numerator V open parentheses t close parentheses minus V open parentheses t subscript 1 close parentheses over denominator t minus t subscript 1 end fraction end style. Jika begin mathsize 14px style V open parentheses t close parentheses equals 3 comma 6 cross times 10 to the power of negative 5 end exponent πt cubed end style, berapakah laju penambahan volume bola pada waktu mendekati 10 detik setelah dipompa? 

     

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L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

laju penambahan volume bola adalah begin mathsize 14px style 4 comma 8 cross times 10 to the power of negative 3 end exponent straight pi space bevelled cm cubed over detik end style 

Pembahasan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell V open parentheses t close parentheses end cell equals cell 3 comma 6 cross times 10 to the power of negative 5 end exponent πt cubed end cell row cell t subscript 1 end cell equals 10 end table end style 

laju penambahan volume bola adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row V equals cell limit as t rightwards arrow t subscript 1 of fraction numerator V open parentheses t close parentheses minus V open parentheses t subscript 1 close parentheses over denominator t minus t subscript 1 end fraction end cell row blank equals cell limit as t rightwards arrow 10 of fraction numerator V open parentheses t close parentheses minus V open parentheses 10 close parentheses over denominator t minus 10 end fraction end cell row blank equals cell limit as t rightwards arrow 10 of fraction numerator 3 comma 6 cross times 10 to the power of negative 5 end exponent πt cubed minus 3 comma 6 cross times 10 to the power of negative 5 end exponent straight pi open parentheses 10 close parentheses cubed over denominator t minus 10 end fraction end cell row blank equals cell limit as t rightwards arrow 10 of fraction numerator 3 comma 6 cross times 10 to the power of negative 5 end exponent straight pi open parentheses t cubed minus 10 cubed close parentheses over denominator t minus 10 end fraction end cell row blank equals cell limit as t rightwards arrow 10 of fraction numerator 3 comma 6 cross times 10 to the power of negative 5 end exponent straight pi open parentheses t minus 10 close parentheses open parentheses straight t squared plus 10 straight t plus 100 close parentheses over denominator open parentheses t minus 10 close parentheses end fraction end cell row blank equals cell limit as t rightwards arrow 10 of 3 comma 6 cross times 10 to the power of negative 5 end exponent straight pi open parentheses straight t squared plus 10 straight t plus 100 close parentheses end cell row blank equals cell 3 comma 6 cross times 10 to the power of negative 5 end exponent straight pi open parentheses 10 squared plus 10 open parentheses 10 close parentheses plus 100 close parentheses end cell row blank equals cell 3 comma 6 cross times 10 to the power of negative 5 end exponent straight pi open parentheses 300 close parentheses space end cell row blank equals cell 4 comma 8 cross times 10 to the power of negative 3 end exponent straight pi end cell end table end style  

Jadi laju penambahan volume bola adalah begin mathsize 14px style 4 comma 8 cross times 10 to the power of negative 3 end exponent straight pi space bevelled cm cubed over detik end style 

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