Pertanyaan

Hitung nilai x → 1 lim ( x 2 − 1 2 − x − 1 1 ) = …

Hitung nilai $x \to 1 lim (\frac{2}{x ^{2} - 1} - \frac{1}{x - 1}) = \dots$

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H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai

nilai $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 2 over denominator x squared minus 1 end fraction minus fraction numerator 1 over denominator x minus 1 end fraction close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table$

Pembahasan

Nilai limit fungsi tersebut dapat ditentukan sebagai berikut. Dengan demikian, nilai

Nilai limit fungsi tersebut dapat ditentukan sebagai berikut.

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

Dengan demikian, nilai $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 2 over denominator x squared minus 1 end fraction minus fraction numerator 1 over denominator x minus 1 end fraction close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table$