Roboguru

Nilai dari

Pertanyaan

Nilai dari begin mathsize 14px style limit as straight x rightwards arrow 0 of fraction numerator 3 minus square root of 2 straight x plus 9 end root over denominator straight x end fraction equals.... end style 

Pembahasan Soal:

Dengan metode perkalian sekawan, maka penyelesaiannya adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow 0 of fraction numerator 3 minus square root of 2 straight x plus 9 end root over denominator straight x end fraction end cell equals cell limit as straight x rightwards arrow 0 of fraction numerator 3 minus square root of 2 straight x plus 9 end root over denominator straight x end fraction times fraction numerator left parenthesis 3 plus square root of 2 straight x plus 9 end root right parenthesis over denominator left parenthesis 3 plus square root of 2 straight x plus 9 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of fraction numerator 9 minus left parenthesis 2 straight x plus 9 right parenthesis over denominator straight x left parenthesis 3 plus square root of 2 straight x plus 9 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of fraction numerator 9 minus 2 straight x minus 9 over denominator straight x left parenthesis 3 plus square root of 2 straight x plus 9 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of fraction numerator negative 2 straight x over denominator straight x left parenthesis 3 plus square root of 2 straight x plus 9 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of fraction numerator negative 2 over denominator left parenthesis 3 plus square root of 2 straight x plus 9 end root right parenthesis end fraction end cell row blank equals cell fraction numerator negative 2 over denominator left parenthesis 3 plus square root of 2 times 0 plus 9 end root right parenthesis end fraction end cell row blank equals cell fraction numerator negative 2 over denominator left parenthesis 3 plus square root of 9 right parenthesis end fraction end cell row blank equals cell fraction numerator negative 2 over denominator left parenthesis 3 plus 3 right parenthesis end fraction end cell row blank equals cell fraction numerator negative 2 over denominator 6 end fraction end cell row blank equals cell negative 1 third end cell end table end style 

Jadi, Nilai begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 minus square root of 2 straight x plus 9 end root over denominator straight x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third end cell end table end style 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. RGFLLIMA

Terakhir diupdate 30 April 2021

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Pertanyaan yang serupa

Tentukan nilai

Pembahasan Soal:

begin mathsize 14px style limit as x rightwards arrow 6 of space fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction equals limit as x rightwards arrow 6 of space fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction times fraction numerator square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root over denominator square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root end fraction space space space space space space space space space space space space space space space space space space space space 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 6 of space fraction numerator open parentheses 3 x minus 2 close parentheses minus open parentheses 2 x plus 4 close parentheses over denominator open parentheses x minus 6 close parentheses open parentheses square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root close parentheses end fraction space space space space space space space space space space space space space space space space space space space space 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 6 of space fraction numerator 3 x minus 2 minus 2 x minus 4 over denominator left parenthesis x minus 6 right parenthesis left parenthesis square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root 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 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 6 of space fraction numerator x minus 6 over denominator left parenthesis x minus 6 right parenthesis left parenthesis square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root 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 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 6 of space fraction numerator 1 over denominator left parenthesis square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root 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 space space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator left parenthesis square root of 3 open parentheses 6 close parentheses minus 2 end root plus square root of 2 open parentheses 6 close parentheses plus 4 end root 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 space space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator left parenthesis square root of 18 minus 2 end root plus square root of 12 plus 4 end root 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 space space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator left parenthesis square root of 16 plus square root of 16 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 space space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator left parenthesis 4 plus 4 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 space space space space space space space space space space space space space space space space space space space space equals 1 over 8 end style  

Jadi, begin mathsize 14px style limit as x rightwards arrow 6 of space fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction equals 1 over 8 end style.

0

Roboguru

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow 2 of fraction numerator straight x squared minus 4 over denominator square root of 4 straight x plus 1 end root minus 3 end fraction end cell equals cell limit as straight x rightwards arrow 2 of fraction numerator straight x squared minus 4 over denominator square root of 4 straight x plus 1 end root minus 3 end fraction cross times fraction numerator square root of 4 straight x plus 1 end root plus 3 over denominator square root of 4 straight x plus 1 end root plus 3 end fraction end cell row blank equals cell limit as straight x rightwards arrow 2 of fraction numerator open parentheses straight x squared minus 4 close parentheses open parentheses square root of 4 straight x plus 1 end root plus 3 close parentheses over denominator 4 straight x plus 1 minus 3 squared end fraction end cell row blank equals cell limit as straight x rightwards arrow 2 of fraction numerator open parentheses straight x minus 2 close parentheses left parenthesis straight x plus 2 right parenthesis open parentheses square root of 4 straight x plus 1 end root plus 3 close parentheses over denominator 4 straight x minus 8 end fraction end cell row blank equals cell limit as straight x rightwards arrow 2 of fraction numerator up diagonal strike open parentheses straight x minus 2 close parentheses end strike left parenthesis straight x plus 2 right parenthesis open parentheses square root of 4 straight x plus 1 end root plus 3 close parentheses over denominator 4 up diagonal strike left parenthesis straight x minus 2 right parenthesis end strike end fraction end cell row blank equals cell limit as straight x rightwards arrow 2 of fraction numerator left parenthesis straight x plus 2 right parenthesis open parentheses square root of 4 straight x plus 1 end root plus 3 close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator left parenthesis left parenthesis 2 right parenthesis plus 2 right parenthesis open parentheses square root of 4 left parenthesis 2 right parenthesis plus 1 end root plus 3 close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator 4 times 6 over denominator 4 end fraction end cell row blank equals 6 end table

Jadi, hasil limit fungsi pada soal tersebut adalah 6.

0

Roboguru

Nilai  adalah ....

Pembahasan Soal:

Kita coba dengan mensubstitusikan nilai begin mathsize 14px style x equals 6 end style ke begin mathsize 14px style limit as x rightwards arrow 6 of open parentheses fraction numerator 2 square root of 6 square root of x minus 12 over denominator x minus 6 end fraction close parentheses end style, sehingga

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 6 of open parentheses fraction numerator 2 square root of 6 square root of x minus 12 over denominator x minus 6 end fraction close parentheses end cell equals cell fraction numerator 2 square root of 6 square root of 6 minus 12 over denominator 6 minus 6 end fraction end cell row blank equals cell fraction numerator 2 times 6 minus 12 over denominator 6 minus 6 end fraction end cell row blank equals cell 0 over 0 end cell end table end style 

Berdasarkan perhitungan, didapat hasil undefined 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 6 of open parentheses fraction numerator 2 square root of 6 square root of x minus 12 over denominator x minus 6 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 2 square root of 6 x end root minus 12 over denominator x minus 6 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses open parentheses fraction numerator 2 square root of 6 x end root minus 12 over denominator x minus 6 end fraction close parentheses open parentheses fraction numerator 2 square root of 6 x end root plus 12 over denominator 2 square root of 6 x end root plus 12 end fraction close parentheses close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator open parentheses 2 square root of 6 x end root close parentheses squared minus 12 squared over denominator open parentheses x minus 6 close parentheses open parentheses 2 square root of 6 x end root plus 12 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 4 times 6 x minus 144 over denominator open parentheses x minus 6 close parentheses open parentheses 2 square root of 6 x end root plus 12 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 24 x minus 144 over denominator open parentheses x minus 6 close parentheses open parentheses 2 square root of 6 x end root plus 12 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 24 open parentheses x minus 6 close parentheses over denominator open parentheses x minus 6 close parentheses open parentheses 2 square root of 6 x end root plus 12 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 24 open parentheses up diagonal strike x minus 6 end strike close parentheses over denominator open parentheses up diagonal strike x minus 6 end strike close parentheses open parentheses 2 square root of 6 x end root plus 12 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 24 over denominator 2 square root of 6 x end root plus 12 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 24 over denominator 2 open parentheses square root of 6 x end root plus 6 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator up diagonal strike 24 over denominator up diagonal strike 2 open parentheses square root of 6 x end root plus 6 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 12 over denominator square root of 6 x end root plus 6 end fraction close parentheses end cell end table end style 

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

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 6 of open parentheses fraction numerator 2 square root of 6 square root of x minus 12 over denominator x minus 6 end fraction close parentheses end cell equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 12 over denominator square root of 6 x end root plus 6 end fraction close parentheses end cell row blank equals cell fraction numerator 12 over denominator square root of 6 left parenthesis 6 right parenthesis end root plus 6 end fraction end cell row blank equals cell fraction numerator 12 over denominator square root of 36 plus 6 end fraction end cell row blank equals cell fraction numerator 12 over denominator 6 plus 6 end fraction end cell row blank equals cell 12 over 12 end cell row blank equals 1 end table end style 

Jadi, nilai dari begin mathsize 14px style stack bold l bold i bold m with bold x bold rightwards arrow bold 6 below space fraction numerator bold 2 square root of bold 6 square root of bold x bold minus bold 12 over denominator bold x bold minus bold 6 end fraction end style adalah begin mathsize 14px style bold 1 end style.undefined

0

Roboguru

Nilai dari x→2lim​x2+x−63−x+7​​ adalah....

Pembahasan Soal:

Dengan menggunakan metode mengalikan akar sekawan, diperoleh

limx2x2+x63x+7========limx2x2+x63x+7×3+x+73+x+7limx2(x+3)(x2)(3+x+7)9(x+7)limx2(x+3)(x2)(3+x+7)x+2limx2(x+3)(x2)(3+x+7)(x2)limx2(x+3)(3+x+7)1(2+3)(3+2+7)1(5)(6)1301

Dengan demikian, nilai dari x2limx2+x63x+7=301.

0

Roboguru

Latihan Tentukan nilai limit dari

Pembahasan Soal:

Perhatikan perhitungan berikut.

begin mathsize 14px style limit as x rightwards arrow 5 of space fraction numerator 4 minus square root of x squared minus 9 end root over denominator 5 minus x end fraction equals limit as x rightwards arrow 5 of space fraction numerator 4 minus square root of x squared minus 9 end root over denominator 5 minus x end fraction cross times fraction numerator 4 plus square root of x squared minus 9 end root over denominator 4 plus square root of x squared minus 9 end root end fraction equals limit as x rightwards arrow 5 of space fraction numerator 4 squared minus open parentheses x squared minus 9 close parentheses over denominator open parentheses 5 minus x close parentheses space open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals limit as x rightwards arrow 5 of space fraction numerator 25 minus x squared over denominator open parentheses 5 minus x close parentheses space open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals limit as x rightwards arrow 5 of space fraction numerator open parentheses 5 minus x close parentheses open parentheses 5 plus x close parentheses over denominator open parentheses 5 minus x close parentheses space open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals limit as x rightwards arrow 5 of space fraction numerator open parentheses 5 plus x close parentheses over denominator open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals fraction numerator open parentheses 5 plus 5 close parentheses over denominator open parentheses 4 plus square root of 5 squared minus 9 end root close parentheses end fraction equals 10 over 8 equals 5 over 4 end style 

Jadi diperoleh nilai limit as x rightwards arrow 5 of space fraction numerator 4 minus square root of x squared minus 9 end root over denominator 5 minus x end fraction equals 5 over 4.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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