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Hasil dari x→1lim​x+4​−6−x​3x2+2x−5​ adalah ....

Pertanyaan

Hasil dari limit as x rightwards arrow 1 of fraction numerator 3 x squared plus 2 x minus 5 over denominator square root of x plus 4 end root minus square root of 6 minus x end root end fraction adalah ....

  1. 4 square root of 5  

  2. 6 square root of 5 

  3. 8 square root of 5 

  4. 10 square root of 5 

  5. 16 square root of 5 

R. Tri

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa jika dilakukan substitusi x equals 1 comma maka didapatkan hasil 0 over 0 sehingga perlu dicari cara lain untuk mencari nilai limitnya.

Perhatikan perhitungan berikut!

limit as x rightwards arrow 1 of fraction numerator 3 x squared plus 2 x minus 5 over denominator square root of x plus 4 end root minus square root of 6 minus x end root end fraction equals limit as x rightwards arrow 1 of open parentheses fraction numerator 3 x squared plus 2 x minus 5 over denominator square root of x plus 4 end root minus square root of 6 minus x end root end fraction times fraction numerator square root of x plus 4 end root plus square root of 6 minus x end root over denominator square root of x plus 4 end root plus square root of 6 minus x end root end fraction close parentheses equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x squared plus 2 x minus 5 close parentheses open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses over denominator open parentheses square root of x plus 4 end root close parentheses squared minus open parentheses square root of 6 minus x end root close parentheses squared end fraction equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x squared plus 2 x minus 5 close parentheses open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses over denominator open parentheses x plus 4 close parentheses minus open parentheses 6 minus x close parentheses end fraction equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x squared plus 2 x minus 5 close parentheses open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses over denominator x plus 4 minus 6 plus x end fraction equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x squared plus 2 x minus 5 close parentheses open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses over denominator 2 x minus 2 end fraction equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x squared plus 2 x minus 5 close parentheses open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses over denominator 2 open parentheses x minus 1 close parentheses end fraction equals limit as x rightwards arrow 1 of fraction numerator 3 x squared plus 2 x minus 5 over denominator 2 open parentheses x minus 1 close parentheses end fraction times limit as x rightwards arrow 1 of open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x plus 5 close parentheses open parentheses x minus 1 close parentheses over denominator 2 open parentheses x minus 1 close parentheses end fraction times limit as x rightwards arrow 1 of open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses equals open parentheses limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x plus 5 close parentheses open parentheses x minus 1 close parentheses over denominator 2 open parentheses x minus 1 close parentheses end fraction close parentheses times open parentheses square root of 1 plus 4 end root plus square root of 6 minus 1 end root close parentheses equals open parentheses limit as x rightwards arrow 1 of fraction numerator 3 x plus 5 over denominator 2 end fraction close parentheses times open parentheses square root of 5 plus square root of 5 close parentheses equals fraction numerator 3 open parentheses 1 close parentheses plus 5 over denominator 2 end fraction times 2 square root of 5 equals fraction numerator 3 plus 5 over denominator 2 end fraction times 2 square root of 5 equals 8 over 2 times 2 square root of 5 equals 8 over 2 times 2 square root of 5 equals 8 square root of 5

Jadi, jawaban yang tepat adalah C.

62

5.0 (2 rating)

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