Roboguru

Nilai dari  adalah...

Pertanyaan

Nilai dari limit as x rightwards arrow square root of 2 of space fraction numerator x squared minus 2 over denominator x minus square root of 2 end fraction adalah...

Pembahasan Soal:

Dengan menggunakan metode perkalian akar sekawan diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow square root of 2 of space fraction numerator x squared minus 2 over denominator x minus square root of 2 end fraction end cell equals cell limit as x rightwards arrow square root of 2 of space fraction numerator x squared minus 2 over denominator x minus square root of 2 end fraction cross times fraction numerator x plus square root of 2 over denominator x plus square root of 2 end fraction end cell row blank equals cell limit as x rightwards arrow square root of 2 of space fraction numerator open parentheses x squared minus 2 close parentheses open parentheses x plus square root of 2 close parentheses over denominator x squared minus 2 end fraction end cell row blank equals cell limit as x rightwards arrow square root of 2 of space open parentheses x plus square root of 2 close parentheses end cell row blank equals cell square root of 2 plus square root of 2 end cell row blank equals cell 2 square root of 2 end cell end table

Dengan demikian nilai dari limit as x rightwards arrow square root of 2 of space fraction numerator x squared minus 2 over denominator x minus square root of 2 end fraction equals 2 square root of 2.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Nur

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Terakhir diupdate 02 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Nilai  adalah ....

Pembahasan Soal:

Dengan mengalikan akar sekawan.

begin mathsize 14px style limit as x rightwards arrow 4 of fraction numerator 4 minus x over denominator square root of 12 minus square root of x plus 8 end root end fraction equals limit as x rightwards arrow 4 of fraction numerator 4 minus x over denominator square root of 12 minus square root of x plus 8 end root end fraction times fraction numerator square root of 12 plus square root of x plus 8 end root over denominator square root of 12 plus square root of x plus 8 end root end fraction equals limit as x rightwards arrow 4 of fraction numerator open parentheses 4 minus x close parentheses open parentheses square root of 12 plus square root of x plus 8 end root close parentheses over denominator 12 minus open parentheses x plus 8 close parentheses end fraction equals limit as x rightwards arrow 4 of fraction numerator up diagonal strike open parentheses 4 minus x close parentheses end strike open parentheses square root of 12 plus square root of x plus 8 end root close parentheses over denominator up diagonal strike open parentheses 4 minus x close parentheses end strike end fraction equals limit as x rightwards arrow 4 of square root of 12 plus square root of x plus 8 end root equals square root of 12 plus square root of 4 plus 8 end root equals square root of 12 plus square root of 12 equals 2 square root of 12 equals 2 square root of 4 times 3 end root equals 2 times 2 square root of 3 equals 4 square root of 3 end style 

Jadi, jawaban yang tepat adalah E.

0

Roboguru

Pembahasan Soal:

limit as x rightwards arrow 1 of fraction numerator 1 minus square root of x over denominator 1 minus x squared end fraction equals limit as x rightwards arrow 1 of fraction numerator 1 minus square root of x over denominator left parenthesis 1 minus x right parenthesis left parenthesis 1 plus x right parenthesis end fraction  space space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow 1 of fraction numerator begin display style 1 minus square root of x end style over denominator begin display style left parenthesis 1 minus square root of x right parenthesis left parenthesis 1 plus square root of x right parenthesis left parenthesis 1 plus x right parenthesis end style end fraction  space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow 1 of fraction numerator begin display style 1 end style over denominator begin display style left parenthesis 1 plus square root of x right parenthesis left parenthesis 1 plus x right parenthesis end style end fraction  space space space space space space space space space space space space space space space space space space space space equals fraction numerator begin display style 1 end style over denominator begin display style left parenthesis 1 plus square root of x right parenthesis left parenthesis 1 plus 1 right parenthesis end style end fraction  space space space space space space space space space space space space space space space space space space space space equals 1 fourth

0

Roboguru

Jika diketahui  tentukan nilai  ?

Pembahasan Soal:

Soal di atas adalah bentuk limit tak tentu dan dapat diselesaikan dengan dalil l'hospital dengan rumus :

begin mathsize 14px style limit as straight x rightwards arrow straight a of fraction numerator straight f open parentheses straight x close parentheses over denominator straight g open parentheses straight x close parentheses end fraction equals limit as straight x rightwards arrow straight a of fraction numerator straight f apostrophe open parentheses straight x close parentheses over denominator straight g apostrophe open parentheses straight x close parentheses end fraction end style 

Maka kita dapat tentukan nilai a :

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as straight x rightwards arrow 3 of fraction numerator ax squared minus 9 straight a over denominator square root of straight x squared plus 16 end root minus 5 end fraction end cell equals 10 row cell limit as straight x rightwards arrow 3 of fraction numerator ax squared minus 9 straight a over denominator open parentheses straight x squared plus 16 close parentheses to the power of begin display style 1 half end style end exponent minus 5 end fraction end cell equals 10 row cell limit as straight x rightwards arrow 3 of fraction numerator 2 ax over denominator begin display style 1 half end style open parentheses straight x squared plus 16 close parentheses to the power of begin display style negative 1 half end style end exponent times 2 straight x end fraction end cell equals 10 row cell fraction numerator 2 straight a open parentheses 3 close parentheses over denominator begin display style 1 half open parentheses open parentheses 3 close parentheses squared plus 16 close parentheses to the power of negative 1 half end exponent times 2 open parentheses 3 close parentheses end style end fraction end cell equals 10 row cell fraction numerator 6 straight a over denominator begin display style 1 half end style open parentheses 25 close parentheses to the power of negative begin display style 1 half end style end exponent times 6 end fraction end cell equals 10 row cell fraction numerator 6 straight a over denominator 3 times fraction numerator 1 over denominator square root of 25 end fraction end fraction end cell equals 10 row cell fraction numerator 6 straight a over denominator begin display style 3 over 5 end style end fraction end cell equals 10 row cell 6 straight a cross times 5 end cell equals cell 10 cross times 3 end cell row cell 30 straight a end cell equals 30 row straight a equals cell 30 over 30 end cell row straight a equals 1 end table end style 

Jadi, nilai begin mathsize 14px style straight a end style adalah 1

Jadi, jawaban yang tepat adalah A

0

Roboguru

Pembahasan Soal:

limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator open parentheses 3 minus square root of x squared plus 5 end root close parentheses end fraction  equals limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator open parentheses 3 minus square root of x squared plus 5 end root close parentheses end fraction cross times fraction numerator 3 plus square root of x squared plus 5 end root over denominator 3 plus square root of x squared plus 5 end root end fraction  equals limit as x rightwards arrow 2 of fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis over denominator left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis end fraction  equals limit as x rightwards arrow 2 of fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis over denominator 9 minus left parenthesis x squared plus 5 right parenthesis end fraction  equals limit as x rightwards arrow 2 of fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis over denominator negative x squared plus 4 end fraction  equals limit as x rightwards arrow 2 of fraction numerator left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis over denominator negative left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis end fraction  equals limit as x rightwards arrow 2 of fraction numerator left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis over denominator negative left parenthesis x plus 2 right parenthesis end fraction  equals fraction numerator open parentheses 3 plus square root of 2 squared plus 5 end root close parentheses over denominator negative left parenthesis 2 plus 2 right parenthesis end fraction  equals negative 3 over 2

0

Roboguru

Pembahasan Soal:

begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction times fraction numerator square root of 4 x plus 1 end root plus square root of 6 x minus 3 end root over denominator square root of 4 x plus 1 end root plus square root of 6 x minus 3 end root end fraction limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals limit as x rightwards arrow 2 of fraction numerator open parentheses 4 x plus 1 close parentheses minus open parentheses 6 x minus 3 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses square root of 4 x plus 1 end root plus square root of 6 x minus 3 end root close parentheses end fraction limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals limit as x rightwards arrow 2 of fraction numerator 4 x plus 1 minus 6 x plus 3 over denominator open parentheses x minus 2 close parentheses open parentheses square root of 4 x plus 1 end root plus square root of 6 x minus 3 end root close parentheses end fraction limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals limit as x rightwards arrow 2 of fraction numerator 4 minus 2 x over denominator open parentheses x minus 2 close parentheses open parentheses square root of 4 x plus 1 end root plus square root of 6 x minus 3 end root close parentheses end fraction limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals limit as x rightwards arrow 2 of fraction numerator negative 2 open parentheses x minus 2 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses square root of 4 x plus 1 end root plus square root of 6 x minus 3 end root close parentheses end fraction limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals limit as x rightwards arrow 2 of fraction numerator negative 2 over denominator open parentheses square root of 4 x plus 1 end root plus square root of 6 x minus 3 end root close parentheses end fraction limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals fraction numerator negative 2 over denominator open parentheses square root of 4 open parentheses 2 close parentheses plus 1 end root plus square root of 6 open parentheses 2 close parentheses minus 3 end root close parentheses end fraction limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals fraction numerator negative 2 over denominator open parentheses square root of 8 plus 1 end root plus square root of 12 minus 3 end root close parentheses end fraction limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals fraction numerator negative 2 over denominator open parentheses square root of 9 plus square root of 9 close parentheses end fraction limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals fraction numerator negative 2 over denominator 3 plus 3 end fraction limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals fraction numerator negative 2 over denominator 6 end fraction limit as x rightwards arrow 2 of fraction numerator square root of 4 x plus 1 end root minus square root of 6 x minus 3 end root over denominator x minus 2 end fraction equals negative 1 third end style 

Jadi, jawaban yang benar adalah begin mathsize 14px style negative 1 third end style.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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