Roboguru

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 6 to the power of x over denominator 2 to the power of x plus 4 to the power of x end fraction equals horizontal ellipsis end style

  1. begin mathsize 14px style horizontal ellipsis end style

  2. begin mathsize 14px style horizontal ellipsis end style

Pembahasan Soal:

Ingatlah bahwa

begin mathsize 14px style limit as x rightwards arrow infinity of a to the power of x equals 0 end style

untuk begin mathsize 14px style negative 1 less than a less than 1 end style.

Untuk menyelesaikan permasalahan limit di atas, kita akan membagi tiap suku dengan begin mathsize 14px style 4 to the power of italic x end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell lim with italic x yields infinity below fraction numerator 6 to the power of italic x over denominator 2 to the power of italic x plus 4 to the power of italic x end fraction end cell equals cell lim with italic x yields infinity below fraction numerator begin display style 6 to the power of italic x over 4 to the power of italic x end style over denominator begin display style 2 to the power of italic x over 4 to the power of italic x plus 4 to the power of italic x over 4 to the power of italic x end style end fraction end cell row blank equals cell lim with italic x yields infinity below fraction numerator open parentheses begin display style 3 over 2 end style close parentheses to the power of italic x over denominator begin display style open parentheses 1 half close parentheses to the power of italic x plus 1 end style end fraction end cell row blank equals cell fraction numerator lim with italic x yields infinity below open parentheses begin display style 3 over 2 end style close parentheses to the power of italic x over denominator begin display style lim with italic x yields infinity below open square brackets open parentheses 1 half close parentheses to the power of italic x plus 1 close square brackets end style end fraction end cell row blank equals cell fraction numerator lim with italic x yields infinity below open parentheses begin display style 3 over 2 end style close parentheses to the power of italic x over denominator 0 plus 1 end fraction end cell row blank equals cell lim with italic x yields infinity below open parentheses 3 over 2 close parentheses to the power of italic x end cell row blank equals infinity end table end style

Dengan demikian, begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 6 to the power of x over denominator 2 to the power of x plus 4 to the power of x end fraction equals infinity end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 15 Maret 2021

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