Pertanyaan

Hitunglah! 5. x → ∞ lim x + x + x x = ...

Hitunglah!

5. $x \to \infty lim \frac{x}{x + x + x} = ...$

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Jawaban terverifikasi

Jawaban

nilai limitnya adalah 1.

Pembahasan

Jadi nilai limitnya adalah 1.

$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 x over denominator square root of x plus square root of x plus square root of x end root end root end fraction cross times fraction numerator begin display style fraction numerator 1 over denominator square root of x end fraction end style over denominator begin display style fraction numerator 1 over denominator square root of x end fraction end style 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 x over denominator square root of x end fraction end style over denominator square root of begin display style x over x end style plus square root of begin display style x over x squared end style plus square root of begin display style x over x to the power of 4 end style end root end root end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 1 over denominator square root of 1 plus square root of 1 over x plus square root of 1 over x cubed end root end root end root end fraction end cell row blank equals cell fraction numerator limit as x rightwards arrow infinity of 1 over denominator square root of limit as x rightwards arrow infinity of 1 plus square root of limit as x rightwards arrow infinity of 1 over x plus square root of limit as x rightwards arrow infinity of 1 over x cubed end root end root end root end fraction end cell row cell Ingat space limit as straight x rightwards arrow infinity of 1 over straight x to the power of straight n end cell equals cell 0 space dan space limit as straight x rightwards arrow infinity of k equals k end cell row blank equals cell fraction numerator 1 over denominator square root of 1 plus square root of 0 plus square root of 0 end root end root end fraction end cell row blank equals cell 1 over 1 end cell row blank equals 1 end table$

Jadi nilai limitnya adalah 1.