Roboguru

Nilai

Pertanyaan

Nilai limit as x rightwards arrow negative 2 of fraction numerator left parenthesis x plus 1 right parenthesis squared minus 1 over denominator x plus 2 end fraction equals....

Pembahasan Soal:

Berdasarkan konsep limit, maka untuk menentukan nilai sutu limit yaitu dengan mensubstitusi nilai x spacex kedalam limit fungsi yang ditentukan sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 of fraction numerator left parenthesis x plus 1 right parenthesis squared minus 1 over denominator x plus 2 end fraction end cell equals cell fraction numerator open parentheses negative 2 plus 1 close parentheses squared minus 1 over denominator negative 2 plus 2 end fraction end cell row cell limit as x rightwards arrow negative 2 of fraction numerator left parenthesis x plus 1 right parenthesis squared minus 1 over denominator x plus 2 end fraction end cell equals cell fraction numerator 1 minus 1 over denominator negative 2 plus 2 end fraction end cell row cell limit as x rightwards arrow negative 2 of fraction numerator left parenthesis x plus 1 right parenthesis squared minus 1 over denominator x plus 2 end fraction end cell equals cell 0 over 0 end cell end table

Karena nilai table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 of fraction numerator left parenthesis x plus 1 right parenthesis squared minus 1 over denominator x plus 2 end fraction end cell equals cell 0 over 0 end cell end table jika menggunakan cara substitusi maka cara selanjutnya yang dapat dilakukan adalah dengan cara pemfaktoran sehingga

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


Jadi nilai limit as x rightwards arrow negative 2 of fraction numerator left parenthesis x plus 1 right parenthesis squared minus 1 over denominator x plus 2 end fraction equals negative 2.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Juni 2021

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