Pertanyaan

Nilai x → ∞ lim 4 x 5 x + 4 − 3 x + 9 = …

Nilai $x \to \infty lim \frac{5 x + 4 - 3 x + 9}{4 x} = \dots$

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Untuk menyelesaikan limit menuju tak hingga , dapat digunakan sifat . Sehingga, Dengan demikian, nilai . Jadi, jawaban yang benar adalah A.

Untuk menyelesaikan limit menuju tak hingga open parentheses x rightwards arrow infinity close parentheses , dapat digunakan sifat limit as x rightwards arrow infinity of 1 over x to the power of n equals 0 . Sehingga,

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator square root of 5 x plus 4 end root minus square root of 3 x plus 9 end root over denominator 4 x end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator square root of 5 x plus 4 end root minus square root of 3 x plus 9 end root over denominator x end fraction end style over denominator begin display style fraction numerator 4 x over denominator x end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator square root of begin display style fraction numerator 5 x plus 4 over denominator x squared end fraction end style end root minus square root of begin display style fraction numerator 3 x plus 9 over denominator x squared end fraction end style end root over denominator 4 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator square root of begin display style 5 over x end style plus begin display style 4 over x squared end style end root minus square root of begin display style 3 over x end style plus begin display style 9 over x squared end style end root over denominator 4 end fraction end cell row blank equals cell fraction numerator square root of begin display style limit as x rightwards arrow infinity of 5 over x plus limit as x rightwards arrow infinity of 4 over x squared end style end root minus square root of begin display style limit as x rightwards arrow infinity of 3 over x plus limit as x rightwards arrow infinity of 9 over x squared end style end root over denominator 4 end fraction end cell row blank equals cell fraction numerator square root of begin display style 5 open parentheses limit as x rightwards arrow infinity of 1 over x close parentheses plus 4 open parentheses limit as x rightwards arrow infinity of 1 over x squared close parentheses end style end root minus square root of begin display style 3 open parentheses limit as x rightwards arrow infinity of 1 over x close parentheses plus 9 open parentheses limit as x rightwards arrow infinity of 1 over x squared close parentheses end style end root over denominator 4 end fraction end cell row blank equals cell fraction numerator square root of 5 open parentheses 0 close parentheses plus 4 open parentheses 0 close parentheses end root minus square root of 3 open parentheses 0 close parentheses plus 9 open parentheses 0 close parentheses end root over denominator 4 end fraction end cell row blank equals 0 end table$

Dengan demikian, nilai $limit as x rightwards arrow infinity of fraction numerator square root of 5 x plus 4 end root minus square root of 3 x plus 9 end root over denominator 4 x end fraction equals 0$ .

Jadi, jawaban yang benar adalah A.