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Gambar dibuat sesuai skala

Jika grafik fungsi tersebut adalah grafik fungsi y equals f left parenthesis x right parenthesis, maka nilai dari:

limit as x rightwards arrow 1 of fraction numerator f left parenthesis x right parenthesis over denominator x minus 1 end fraction

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Pembahasan

  • Menentukan f left parenthesis x right parenthesis

Pada gambar kurva tersebut memotong di sumbu-x pada titik left parenthesis 1 comma 0 right parenthesis comma space open parentheses 13 over 10 space comma space 0 close parentheses dan melalui titik open parentheses 8 over 5 comma 7 over 10 close parentheses

jadi, 

straight y equals straight a left parenthesis straight x minus straight x subscript 1 right parenthesis open parentheses straight x minus straight x subscript 2 close parentheses straight y equals straight a left parenthesis straight x minus 1 right parenthesis open parentheses straight x minus 13 over 10 close parentheses

Selanjutnya menentukan nilai a,

table attributes columnalign right center left columnspacing 0px end attributes row cell 7 over 10 end cell equals cell straight a left parenthesis 8 over 5 minus 1 right parenthesis open parentheses 8 over 5 minus 13 over 10 close parentheses end cell row cell 7 over 10 end cell equals cell straight a open parentheses 3 over 5 close parentheses open parentheses 3 over 10 close parentheses end cell row cell 7 over 10 end cell equals cell straight a 9 over 50 end cell row straight a equals cell 7 over 10 cross times 50 over 9 end cell row straight a equals cell 35 over 9 end cell end table

jadi,

 table attributes columnalign right center left columnspacing 0px end attributes row straight y equals cell straight a left parenthesis straight x minus 1 right parenthesis open parentheses straight x minus 13 over 10 close parentheses end cell row y equals cell 35 over 9 open parentheses x minus 1 close parentheses open parentheses x minus 13 over 10 close parentheses end cell row y equals cell 35 over 9 open parentheses x squared minus 23 over 10 x plus 13 over 10 close parentheses end cell row y equals cell 35 over 9 x squared minus 161 over 18 x plus 91 over 18 end cell row y equals cell 70 x squared minus 161 x plus 91 end cell end table

Jadi, f left parenthesis x right parenthesis equals 70 x squared minus 161 x plus 91

  • Menentukan nilai limit.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator f left parenthesis x right parenthesis over denominator x minus 1 end fraction end cell equals cell limit as x rightwards arrow 1 of fraction numerator 70 x squared minus 161 x plus 91 over denominator x minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 7 left parenthesis 10 x squared minus 23 x plus 13 right parenthesis over denominator x minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 7 left parenthesis x minus 1 right parenthesis open parentheses 10 x minus 13 close parentheses over denominator x minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of 7 open parentheses 10 x minus 13 close parentheses end cell row blank equals cell 7 left parenthesis 10 left parenthesis 1 right parenthesis minus 13 right parenthesis end cell row blank equals cell 7 left parenthesis negative 3 right parenthesis end cell row blank equals cell negative 21 end cell end table

Jadi, nilai limit as x rightwards arrow 1 of fraction numerator f left parenthesis x right parenthesis over denominator x minus 1 end fraction equals negative 21.

 

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