Roboguru

y→2lim​y2+y−6y2−4y+4​

Pertanyaan

begin mathsize 14px style limit as y rightwards arrow 2 of fraction numerator y squared minus 4 y plus 4 over denominator y squared plus y minus 6 end fraction end style

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as y rightwards arrow 2 of fraction numerator y squared minus 4 y plus 4 over denominator y squared plus y minus 6 end fraction end cell equals cell limit as y rightwards arrow 2 of fraction numerator up diagonal strike open parentheses y minus 2 close parentheses end strike. open parentheses y minus 2 close parentheses over denominator up diagonal strike open parentheses y minus 2 close parentheses end strike. open parentheses y plus 3 close parentheses end fraction end cell row blank equals cell limit as y rightwards arrow 2 of fraction numerator open parentheses y minus 2 close parentheses over denominator open parentheses y plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 2 minus 2 over denominator 2 plus 3 end fraction end cell row blank equals cell 0 over 5 end cell row blank equals 0 end table end style

Jadi, jawabannya adalah 0.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 05 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

x→0lim​x2x2+4​−2​

Pembahasan Soal:

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 square root of x squared plus 4 end root minus 2 over denominator x squared end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator square root of x squared plus 4 end root minus 2 over denominator x squared end fraction cross times fraction numerator square root of x squared plus 4 end root plus 2 over denominator square root of x squared plus 4 end root plus 2 end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x squared plus 4 minus 4 over denominator x squared open parentheses square root of x squared plus 4 end root plus 2 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator up diagonal strike x squared end strike over denominator up diagonal strike x squared end strike open parentheses square root of x squared plus 4 end root plus 2 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 1 over denominator square root of x squared plus 4 end root plus 2 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 0 squared plus 4 end root plus 2 end fraction end cell row blank equals cell 1 fourth end cell end table end style

Jadi, jawabannya adalah begin mathsize 14px style bold 1 over bold 4 end style

1

Roboguru

Jika x→alim​f(x)=8, x→alim​g(x)=−5 dan x→alim​h(x)=2. Nilai dari x→alim​4h(x)2f(x)+3g(x)​=...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a of fraction numerator 2 f left parenthesis x right parenthesis plus 3 g left parenthesis x right parenthesis over denominator 4 h left parenthesis x right parenthesis end fraction end cell equals cell fraction numerator limit as x rightwards arrow a of 2 f left parenthesis x right parenthesis plus limit as x rightwards arrow a of 3 g left parenthesis x right parenthesis over denominator limit as x rightwards arrow a of 4 h left parenthesis x right parenthesis end fraction end cell row blank equals cell fraction numerator 2 limit as x rightwards arrow a of f left parenthesis x right parenthesis plus 3 limit as x rightwards arrow a of g left parenthesis x right parenthesis over denominator 4 limit as x rightwards arrow a of h left parenthesis x right parenthesis end fraction end cell row blank equals cell fraction numerator 2 cross times 8 plus 3 cross times left parenthesis negative 5 right parenthesis over denominator 4 cross times 2 end fraction end cell row blank equals cell fraction numerator 16 minus 15 over denominator 8 end fraction end cell row blank equals cell 1 over 8 end cell end table end style 

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow a of fraction numerator 2 f left parenthesis x right parenthesis plus 3 g left parenthesis x right parenthesis over denominator 4 h left parenthesis x right parenthesis end fraction end style adalah begin mathsize 14px style 1 over 8 end style 

0

Roboguru

Nilai x→4lim​x2+9−5​x2−16​=…

Pembahasan Soal:

limit as x rightwards arrow 4 of space fraction numerator x squared minus 16 over denominator square root of x squared plus 9 minus 5 end root end fraction space  equals limit as x rightwards arrow 4 of space fraction numerator x squared minus 16 over denominator open parentheses x squared plus 9 close parentheses to the power of begin display style 1 half end style end exponent minus 5 end fraction  equals limit as x rightwards arrow 4 of space fraction numerator 2 x over denominator begin display style 1 half end style open parentheses x squared plus 9 close parentheses to the power of begin display style negative 1 half end style end exponent.2.5 end fraction  equals stack lim space with x rightwards arrow 4 below space fraction numerator 2 x over denominator begin display style fraction numerator 1 over denominator square root of x squared plus 9 end root end fraction end style minus 5 end fraction  equals fraction numerator 2 open parentheses 4 close parentheses over denominator begin display style fraction numerator 1 over denominator square root of 16 plus 9 end root minus 5 end fraction end style end fraction  equals fraction numerator 8 over denominator begin display style 1 fifth end style minus 8 end fraction  equals fraction numerator 8 over denominator begin display style fraction numerator 1 minus 25 over denominator 5 end fraction end style end fraction  equals 8 over 1. fraction numerator 5 over denominator negative 24 end fraction equals negative 5 over 3

1

Roboguru

x→2lim​3−2x4x+1​=....

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of space fraction numerator 4 x plus 1 over denominator 3 minus 2 x end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator 4 open parentheses 2 close parentheses plus 1 over denominator 3 minus 2 open parentheses 2 close parentheses end fraction end cell row blank equals cell fraction numerator 9 over denominator negative 1 end fraction end cell row blank equals cell negative 9 end cell end table end style 

Jadi, nilai dari begin mathsize 14px style limit as x rightwards arrow 2 of space fraction numerator 4 x plus 1 over denominator 3 minus 2 x end fraction equals negative 9 end style.

0

Roboguru

Nilai dari x→1lim​x−1x​−1​=...

Pembahasan Soal:

Jika menggunakan metode substitusi dalam menentukan nilai limit fungsi tersebut maka akan diperoleh undefined seperti berikut ini:

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

Oleh sebab itu, untuk menentukan nilai limit fungsi tersebut salah satunya dapat menggunakan metode perkalian dengan akar sekawan maka diperoleh:

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

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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