Roboguru

Tentukan nilai:

Pertanyaan

Tentukan nilai:

begin mathsize 14px style limit as straight x rightwards arrow negative 1 of fraction numerator straight x plus 1 over denominator 1 minus square root of straight x plus 2 end root end fraction end style 

Pembahasan Soal:

Dengan menerapakan konsep perkalian sekawan, maka diperoleh:

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

Jadi, begin mathsize 14px style limit as straight x rightwards arrow negative 1 of fraction numerator straight x plus 1 over denominator 1 minus square root of straight x plus 2 end root end fraction equals negative 2 end style 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. RGFLLIMA

Terakhir diupdate 30 April 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:

Pembahasan:

Untuk menentukan nilai limit suatu fungsi aljabar langkah pertama adalah kita substitusi dari nilai limit pendekatanya, dalam soal ini kita substitusi nilai begin mathsize 14px style x equals 4 end style, sehingga akan kita dapatkan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator x minus 4 over denominator square root of x minus 2 end fraction end cell equals cell fraction numerator open parentheses 4 close parentheses minus 4 over denominator square root of 4 minus 2 end fraction end cell row blank equals cell 0 over 0 end cell end table end style    

Karena nilainya begin mathsize 14px style 0 over 0 end style maka kita coba dengan cara kali akar sekawan, yaitu kita kali dengan begin mathsize 14px style fraction numerator square root of x plus 2 over denominator square root of x plus 2 end fraction end style sehingga akan kita dapatkan hasil sebagai berikut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator x minus 4 over denominator square root of x minus 2 end fraction times fraction numerator square root of x plus 2 over denominator square root of x plus 2 end fraction end cell equals cell space limit as x rightwards arrow 4 of space fraction numerator open parentheses x minus 4 close parentheses open parentheses square root of x plus 2 close parentheses over denominator x plus 2 square root of x minus 2 square root of x minus 4 end fraction end cell row blank equals cell space limit as x rightwards arrow 4 of fraction numerator open parentheses x minus 4 close parentheses open parentheses square root of x plus 2 close parentheses over denominator x minus 4 end fraction end cell row blank equals cell space limit as x rightwards arrow 4 of space square root of x plus 2 end cell row blank equals cell square root of 4 plus 2 end cell row blank equals cell 2 plus 2 end cell row blank equals 4 end table end style 

Sehingga kita dapatkan nilainya limitnya yaitu begin mathsize 14px style 4 end style 

0

Roboguru

Nilai  adalah ...

Pembahasan Soal:

Substitusi x = 1:

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 over denominator square root of 2 plus 2 x end root minus square root of 6 minus 2 x end root end fraction end cell equals cell fraction numerator 1 cubed minus 1 squared over denominator square root of 2 plus 2 times 1 end root minus square root of 6 minus 2 times 1 end root end fraction end cell row blank equals cell fraction numerator 1 minus 1 over denominator square root of 4 minus square root of 4 end fraction end cell row blank equals cell 0 over 0 space open parentheses tak space tentu close parentheses end cell end table

Karena 0 over 0 merupakan bentuk tak tentu, maka tidak boleh. Jadi harus diselesaiakan dengan metode mengalikan akar sekawan: (ingat: open parentheses a plus b close parentheses open parentheses a minus b close parentheses equals a squared minus b squared)

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

Jadi, jawaban yang tepat adalah D

0

Roboguru

Tentukan nilai limit dari fungsi-fungsi berikut ini:

Pembahasan Soal:

Dengan menggunakan metode mengalikan akar sekawan, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator 5 x over denominator square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x plus 1 end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of open parentheses fraction numerator 5 x over denominator square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x plus 1 end root end fraction times fraction numerator square root of x squared minus 2 x plus 1 end root plus square root of x squared plus 3 x plus 1 end root over denominator square root of x squared minus 2 x plus 1 end root plus square root of x squared plus 3 x plus 1 end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses 5 x close parentheses open parentheses square root of x squared minus 2 x plus 1 end root plus square root of x squared plus 3 x plus 1 end root close parentheses over denominator open parentheses x squared minus 2 x plus 1 close parentheses minus open parentheses x squared plus 3 x plus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses 5 x close parentheses open parentheses square root of x squared minus 2 x plus 1 end root plus square root of x squared plus 3 x plus 1 end root close parentheses over denominator x squared minus 2 x plus 1 minus x squared minus 3 x minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses 5 x close parentheses open parentheses square root of x squared minus 2 x plus 1 end root plus square root of x squared plus 3 x plus 1 end root close parentheses over denominator negative 5 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses square root of x squared minus 2 x plus 1 end root plus square root of x squared plus 3 x plus 1 end root close parentheses over denominator negative 1 end fraction end cell row blank equals cell fraction numerator square root of 0 squared minus 2 open parentheses 0 close parentheses plus 1 end root plus square root of 0 squared plus 3 open parentheses 0 close parentheses plus 1 end root over denominator negative 1 end fraction end cell row blank equals cell fraction numerator square root of 1 plus square root of 1 over denominator negative 1 end fraction end cell row blank equals cell fraction numerator 1 plus 1 over denominator negative 1 end fraction end cell row blank equals cell fraction numerator 2 over denominator negative 1 end fraction end cell row blank equals cell negative 2 end cell end table end style 

Jadi nilai dari begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator 5 x over denominator square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x plus 1 end root end fraction end style adalah begin mathsize 14px style negative 2 end style

0

Roboguru

Nilai

Pembahasan Soal:

space limit as x rightwards arrow 3 of space fraction numerator 2 minus square root of x plus 1 end root over denominator x minus 3 end fraction space. space fraction numerator 2 plus square root of x plus 1 end root over denominator 2 plus square root of x plus 1 end root end fraction  space limit as x rightwards arrow 3 of space fraction numerator 4 minus left parenthesis x plus 1 right parenthesis over denominator open parentheses x minus 3 close parentheses open parentheses 2 plus square root of x plus 1 end root close parentheses end fraction  limit as x rightwards arrow 3 of fraction numerator up diagonal strike open parentheses negative x plus 3 close parentheses end strike over denominator negative up diagonal strike open parentheses negative x plus 3 close parentheses end strike open parentheses 2 plus square root of x plus 1 end root close parentheses end fraction  limit as x rightwards arrow 3 of fraction numerator 1 over denominator negative left parenthesis 2 plus square root of x plus 1 right parenthesis end root end fraction  equals fraction numerator 1 over denominator negative open parentheses 2 plus square root of 3 plus 1 end root close parentheses end fraction  equals fraction numerator 1 over denominator negative left parenthesis 2 plus 2 right parenthesis end fraction  equals negative 1 fourth

1

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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