Pertanyaan

Tentukan nilai dari x → 2 1 lim 2 x 2 + x − 1 2 x 2 + 7 x − 4

Tentukan nilai dari $x \to \frac{1}{2} lim \frac{2 x ^{2} + 7 x - 4}{2 x ^{2} + x - 1}$

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Jawaban terverifikasi

Jawaban

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$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 half of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x squared plus 7 x minus 4 over denominator 2 x squared plus x minus 1 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table end style$ .

Pembahasan

Subtitusi nilai dengan : Karena hasil tidak terdefinisi, maka digunakan pemfaktoran berikut: Jadi, .

Subtitusi nilai dengan :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 half of fraction numerator 2 x squared plus 7 x minus 4 over denominator 2 x squared plus x minus 1 end fraction end cell equals cell fraction numerator 2 left parenthesis 1 half right parenthesis squared plus 7 times 1 half minus 4 over denominator 2 left parenthesis 1 half right parenthesis squared plus 1 half minus 1 end fraction end cell row blank equals cell fraction numerator begin display style 1 half plus 7 over 2 minus 8 over 2 end style over denominator 1 half plus 1 half minus 1 end fraction end cell row blank equals cell fraction numerator begin display style 0 end style over denominator 0 end fraction end cell end table end style$

Karena hasil tidak terdefinisi, maka digunakan pemfaktoran berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 half of fraction numerator 2 x squared plus 7 x minus 4 over denominator 2 x squared plus x minus 1 end fraction end cell equals cell limit as x rightwards arrow 1 half of fraction numerator left parenthesis 2 x minus 1 right parenthesis left parenthesis x plus 4 right parenthesis over denominator left parenthesis 2 x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 1 half of fraction numerator left parenthesis x plus 4 right parenthesis over denominator left parenthesis x plus 1 right parenthesis end fraction end cell row blank equals cell fraction numerator 1 half plus 4 over denominator 1 half plus 1 end fraction end cell row blank equals cell fraction numerator 9 over 2 over denominator 3 over 2 end fraction end cell row blank equals cell 9 over 2 times 2 over 3 end cell row blank equals 3 end table end style$

Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 half of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x squared plus 7 x minus 4 over denominator 2 x squared plus x minus 1 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table end style$ .