Pertanyaan

x → 5 lim x 2 + 3 − 2 x − 1

$x \to 5 lim \frac{x - 1}{x ^{2} + 3 - 2}$

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S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

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$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow thin space 5 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator x minus 1 over denominator square root of x squared plus 3 end root minus 2 end fraction close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 7 plus 1 over denominator 3 end fraction end cell end table end style$ .

Pembahasan

Diketahui: Sehingga didapat: Jadi, .

Diketahui:

$begin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator x minus 1 over denominator square root of x squared plus 3 end root minus 2 end fraction end style$

Sehingga didapat:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow thin space 5 of open parentheses fraction numerator x minus 1 over denominator square root of x squared plus 3 end root minus 2 end fraction close parentheses end cell equals cell fraction numerator 5 minus 1 over denominator square root of 5 squared plus 3 end root minus 2 end fraction end cell row blank equals cell fraction numerator 4 over denominator square root of 28 minus 2 end fraction end cell row blank equals cell fraction numerator 4 over denominator square root of 2 squared times 7 end root minus 2 end fraction end cell row blank equals cell fraction numerator 4 over denominator 2 square root of 7 minus 2 end fraction end cell row blank equals cell fraction numerator 4 over denominator 2 open parentheses square root of 7 minus 1 close parentheses end fraction end cell row blank equals cell fraction numerator 2 over denominator open parentheses square root of 7 minus 1 close parentheses end fraction cross times fraction numerator square root of 7 plus 1 over denominator square root of 7 plus 1 end fraction end cell row blank equals cell fraction numerator 2 open parentheses square root of 7 plus 1 close parentheses over denominator open parentheses 7 minus 1 close parentheses end fraction end cell row blank equals cell fraction numerator 2 open parentheses square root of 7 plus 1 close parentheses over denominator 6 end fraction end cell row blank equals cell fraction numerator square root of 7 plus 1 over denominator 3 end fraction end cell end table end style$

Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow thin space 5 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator x minus 1 over denominator square root of x squared plus 3 end root minus 2 end fraction close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 7 plus 1 over denominator 3 end fraction end cell end table end style$ .