Pertanyaan

Nilai x → ∞ lim cos x 1 sin x 2 + cos x 3 = ....

Nilai $x \to \infty lim \frac{sin \frac{2}{x} + cos \frac{3}{x}}{cos \frac{1}{x}} = ....$

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Jawaban terverifikasi

Jawaban

Nilai dari

Nilai dari $begin mathsize 14px style limit as straight x rightwards arrow infinity of fraction numerator sin begin display style 2 over straight x end style plus cos begin display style 3 over straight x end style over denominator cos begin display style 1 over straight x end style end fraction equals 1 end style$

Pembahasan

Limit trigonometritak hingga. Misalkan maka: Jika maka Jadi, Nilai dari

Limit trigonometri tak hingga.

Misalkan y equals 1 over x maka:

Jika x rightwards arrow infinity maka y rightwards arrow 0

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow infinity of fraction numerator sin begin display style 2 over straight x end style plus cos begin display style 3 over straight x end style over denominator cos begin display style 1 over straight x end style end fraction end cell equals cell limit as straight y rightwards arrow 0 of fraction numerator sin space begin display style 2 straight y end style plus cos begin display style 3 straight y end style over denominator cos space straight y end fraction end cell row blank equals cell fraction numerator sin space left parenthesis 2 times 0 right parenthesis plus cos left parenthesis 3 times 0 right parenthesis over denominator cos space 0 end fraction end cell row blank equals cell fraction numerator sin space left parenthesis 0 right parenthesis plus cos left parenthesis 0 right parenthesis over denominator cos space 0 end fraction end cell row blank equals cell fraction numerator 0 plus 1 over denominator 1 end fraction end cell row blank equals 1 end table$

Jadi, Nilai dari $begin mathsize 14px style limit as straight x rightwards arrow infinity of fraction numerator sin begin display style 2 over straight x end style plus cos begin display style 3 over straight x end style over denominator cos begin display style 1 over straight x end style end fraction equals 1 end style$