Pertanyaan

Tentukan nilai dari x → ∞ lim tan x 1 x ( 1 − cos x 4 ) .

Tentukan nilai dari $x \to \infty lim \frac{x ( 1 - cos \frac{4}{x} )}{tan \frac{1}{x}}$ .

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Misalkan Untuk mendekati maka mendekati 0. Bentuk Jadi, nilai dari adalah 8

Misalkan 1 over x equals y

Untuk mendekati infinity maka mendekati 0.

Bentuk 1 minus cos space 4 y equals 2 space sin squared 2 y

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator x open parentheses 1 minus cos space begin display style 4 over x end style close parentheses over denominator tan space begin display style 1 over x end style end fraction end cell equals cell limit as y rightwards arrow 0 of fraction numerator begin display style 1 over y end style open parentheses 1 minus co s space 4 y close parentheses over denominator tan space y end fraction end cell row blank equals cell limit as y rightwards arrow 0 of fraction numerator begin display style 1 over y end style open parentheses 2 sin squared space 2 y close parentheses over denominator tan space begin display style y end style end fraction end cell row blank equals cell limit as y rightwards arrow 0 of fraction numerator open parentheses 2 space sin squared begin display style space 2 y end style close parentheses over denominator space y space tan begin display style y space end style end fraction end cell row blank equals cell limit as y rightwards arrow 0 of space 2 times fraction numerator sin space 2 y over denominator y end fraction times fraction numerator sin space 2 y over denominator tan space begin display style y end style end fraction end cell row blank equals cell 2 times 2 times 2 end cell row blank equals 8 end table$

Jadi, nilai dari $limit as x rightwards arrow infinity of fraction numerator x open parentheses 1 minus cos space begin display style 4 over x end style close parentheses over denominator tan space begin display style 1 over x end style end fraction$ adalah 8