Roboguru

Nilai

Pertanyaan

Nilai limit as x rightwards arrow infinity of fraction numerator 8 space sin space begin display style 3 over x end style over denominator tan space begin display style 2 over x end style end fraction equals...begin mathsize 14px style space end style 

  1. 4space 

  2. 24space 

  3. 16space 

  4. 12space 

Pembahasan Soal:

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin space begin display style a x end style over denominator tan space b x end fraction end cell equals cell a over b end cell row cell limit as x rightwards arrow 0 of fraction numerator k times sin space begin display style x end style over denominator tan space x end fraction end cell equals cell k times limit as x rightwards arrow 0 of fraction numerator sin space begin display style x end style over denominator tan space x end fraction equals k times 1 equals k end cell end table  

Diketahui limit as x rightwards arrow infinity of fraction numerator 8 space sin space begin display style 3 over x end style over denominator tan space begin display style 2 over x end style end fraction.

limit as x rightwards arrow infinity of fraction numerator 8 space sin space begin display style 3 over x end style over denominator tan space begin display style 2 over x end style end fraction equals limit as x rightwards arrow infinity of fraction numerator 8 space sin space begin display style 3 1 over x end style over denominator tan space begin display style 2 1 over x end style end fraction

Misalkan:

a equals 1 over x comma space maka space x equals 1 over a x rightwards arrow infinity comma space maka space a rightwards arrow 0 

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 8 space sin space begin display style 3 1 over x end style over denominator tan space begin display style 2 1 over x end style end fraction end cell equals cell limit as a rightwards arrow 0 of fraction numerator 8 space sin space begin display style 3 a end style over denominator tan space begin display style 2 a end style end fraction end cell row blank equals cell 8 times 3 over 2 end cell row blank equals 12 end table 

Sehingga, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 8 space sin space begin display style 3 1 over x end style over denominator tan space begin display style 2 1 over x end style 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 12 end table.

Jadi, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Juni 2021

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