Pertanyaan

Nilai dari x → − 1 lim ( 7 + x − 5 − x 3 x + 3 ) adalah ....

Nilai dari $x \to - 1 lim (\frac{3 x + 3}{7 + x - 5 - x})$ adalah ....

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Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $begin mathsize 14px style bold lim with bold x bold rightwards arrow bold minus bold 1 below space fraction numerator bold 3 bold x bold plus bold 3 over denominator square root of bold 7 bold plus bold x end root bold minus square root of bold 5 bold minus bold x end root end fraction end style$ adalah

Pembahasan

Kita coba dengan mensubstitusikan nilai ke , sehingga Berdasarkan perhitungan, didapat hasil adalah dalam bentuk tak tentu. Untuk menyelesaikan soal tersebut, kita bisa coba dengan memanipulasi soal/pernyataan yang diberikan. Setelah kita manipulasi dan dapat bentuk paling sederhana, kita substitusikan nilai . Jadi, nilai dari adalah .

Kita coba dengan mensubstitusikan nilai ke , sehingga

Berdasarkan perhitungan, didapat hasil adalah dalam bentuk tak tentu.

Untuk menyelesaikan soal tersebut, kita bisa coba dengan memanipulasi soal/pernyataan yang diberikan.

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

Setelah kita manipulasi dan dapat bentuk paling sederhana, kita substitusikan nilai .

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

Jadi, nilai dari $begin mathsize 14px style bold lim with bold x bold rightwards arrow bold minus bold 1 below space fraction numerator bold 3 bold x bold plus bold 3 over denominator square root of bold 7 bold plus bold x end root bold minus square root of bold 5 bold minus bold x end root end fraction end style$ adalah .