Pertanyaan

Nilai x → − 5 lim x + 5 1 − x + 6 adalah ....

Nilai $x \to - 5 lim \frac{1 - x + 6}{x + 5}$ adalah ....

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I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai $begin mathsize 14px style limit as x rightwards arrow negative 5 of fraction numerator 1 minus square root of x plus 6 end root over denominator x plus 5 end fraction end style$ adalah

Pembahasan

Untuk ,maka . Diperoleh nilai . Oleh karena itu, fungsi dalam limit dapat dikalikan dengan sekawannya seperti berikut, Jadi, nilai adalah .

Untuk , maka

$begin mathsize 14px style limit as x rightwards arrow negative 5 of fraction numerator 1 minus square root of x plus 6 end root over denominator x plus 5 end fraction equals fraction numerator 1 minus square root of negative 5 plus 6 end root over denominator negative 5 plus 5 end fraction equals fraction numerator 1 minus 1 over denominator 0 end fraction equals 0 over 0 end style$ .

Diperoleh nilai . Oleh karena itu, fungsi dalam limit dapat dikalikan dengan sekawannya seperti berikut,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow negative 5 of fraction numerator 1 minus square root of x plus 6 end root over denominator x plus 5 end fraction end cell row blank equals cell limit as x rightwards arrow negative 5 of fraction numerator 1 minus square root of x plus 6 end root over denominator x plus 5 end fraction times fraction numerator 1 plus square root of x plus 6 end root over denominator 1 plus square root of x plus 6 end root end fraction end cell row blank equals cell limit as x rightwards arrow negative 5 of space fraction numerator 1 minus left parenthesis x plus 6 right parenthesis over denominator open parentheses x plus 5 close parentheses open parentheses 1 plus square root of x plus 6 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 5 of space fraction numerator negative 5 minus x over denominator left parenthesis x plus 5 right parenthesis open parentheses 1 plus square root of x plus 6 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 5 of space fraction numerator negative up diagonal strike left parenthesis x plus 5 right parenthesis end strike over denominator up diagonal strike left parenthesis x plus 5 right parenthesis end strike open parentheses 1 plus square root of x plus 6 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 5 of space fraction numerator negative 1 over denominator 1 plus square root of x plus 6 end root end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 1 plus square root of negative 5 plus 6 end root end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 1 plus square root of 1 end fraction end cell row blank equals cell negative 1 half end cell end table end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow negative 5 of fraction numerator 1 minus square root of x plus 6 end root over denominator x plus 5 end fraction end style$ adalah .

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