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Nilai dari

Pertanyaan

Nilai dari limit as x rightwards arrow 1 of fraction numerator x cubed minus x squared minus x plus 1 over denominator x minus 2 square root of x plus 1 end fraction equals....  

  1. 20 

  2. 16 

  3. 8 

  4. 4 

  5. 2 

Pembahasan Soal:

Dengan menggunakna metode L'hospital.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator x cubed minus x squared minus x plus 1 over denominator x minus 2 square root of x plus 1 end fraction end cell equals cell limit as x rightwards arrow 1 of fraction numerator x cubed minus x squared minus x plus 1 over denominator x minus 2 x to the power of begin display style 1 half end style end exponent plus 1 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 3 x squared minus 2 x minus 1 over denominator 1 minus 2 times begin display style 1 half end style x to the power of begin display style 1 half end style minus 1 end exponent end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 3 x squared minus 2 x minus 1 over denominator 1 minus x to the power of begin display style negative 1 half end style end exponent end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 6 x minus 2 over denominator negative 1 times open parentheses negative begin display style 1 half end style close parentheses x to the power of begin display style negative 1 half minus 1 end style end exponent end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 6 x minus 2 over denominator begin display style 1 half end style x to the power of begin display style negative 3 over 2 end style end exponent end fraction end cell row blank equals cell fraction numerator 6 times 1 minus 2 over denominator 1 half open parentheses 1 close parentheses to the power of negative 3 over 2 end exponent end fraction end cell row blank equals cell fraction numerator 4 over denominator begin display style 1 half end style end fraction end cell row blank equals cell 4 cross times 2 over 1 end cell row blank equals 8 end table  

Jadi, jawaban yang tepat adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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