Pertanyaan

Nilai x → 0 lim 1 − 3 1 − x 1 − x − 1 adalah ...

Nilai $x \to 0 lim \frac{1 - x - 1}{1 - 3 1 - x}$ adalah ...

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Limit merupakan sebuah konsep matematika dimana sesuatu dikatakan "hampir" atau "mendekati" nilai suatu bilangan tertentu. Dengan menggunakan dalil L'Hopital, dimana: maka tentukan turunan dari dan . Turunan fungsi : Turunan fungsi : Nilai : Sehingga, nilai dari adalah . Jadi, jawaban yang tepat adalah E.

Limit merupakan sebuah konsep matematika dimana sesuatu dikatakan "hampir" atau "mendekati" nilai suatu bilangan tertentu.

Dengan menggunakan dalil L'Hopital, dimana:

$begin mathsize 14px style limit as x rightwards arrow a of fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals limit as x rightwards arrow a of fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction end style$

maka tentukan turunan dari dan .

Turunan fungsi :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell square root of 1 minus x end root minus 1 end cell row y equals cell open parentheses 1 minus x close parentheses to the power of begin inline style 1 half end style end exponent minus 1 end cell row cell y apostrophe end cell equals cell negative 1 half open parentheses 1 minus x close parentheses to the power of 1 half minus 1 end exponent end cell row cell y apostrophe end cell equals cell negative 1 half open parentheses 1 minus x close parentheses to the power of begin inline style negative 1 half end style end exponent end cell row cell y apostrophe end cell equals cell fraction numerator 1 over denominator negative 2 square root of 1 minus x end root end fraction end cell end table end style$

Turunan fungsi :

$begin mathsize 14px style y equals 1 minus cube root of 1 minus x end root y equals 1 minus open parentheses 1 minus x close parentheses to the power of begin inline style 1 third end style end exponent y apostrophe equals 1 third open parentheses 1 minus x close parentheses to the power of begin inline style 1 third end style minus 1 end exponent y apostrophe equals 1 third open parentheses 1 minus x close parentheses to the power of begin inline style negative 2 over 3 end style end exponent y apostrophe equals fraction numerator 1 over denominator 3 cube root of open parentheses 1 minus x close parentheses squared end root end fraction end style$

Nilai $begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of 1 minus x end root minus 1 over denominator 1 minus cube root of 1 minus x end root end fraction end style$ :

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

Sehingga, nilai dari $begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of 1 minus x end root minus 1 over denominator 1 minus cube root of 1 minus x end root end fraction end style$ adalah .

Jadi, jawaban yang tepat adalah E.