Pertanyaan

Nilai dari x → ∞ lim x 2 − 4 sin ( 2 x − 4 ) = ...

Nilai dari $x \to \infty lim \frac{sin ( 2 x - 4 )}{x ^{2} - 4} = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari $limit as x rightwards arrow infinity of fraction numerator sin left parenthesis 2 x minus 4 right parenthesis over denominator x squared minus 4 end fraction equals 0$ .

Pembahasan

ingat bahwa Dari soal diperoleh: Jadi, nilai dari .

ingat bahwa $limit as x rightwards arrow infinity of fraction numerator sin space a x over denominator b x end fraction equals 0$

Dari soal diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator sin space left parenthesis 2 x minus 4 right parenthesis over denominator x squared minus 4 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator sin space 2 left parenthesis x minus 2 right parenthesis over denominator left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator sin space 2 left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis end fraction times fraction numerator 1 over denominator x plus 2 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator sin space 2 left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis end fraction times limit as x rightwards arrow infinity of fraction numerator 1 over denominator x plus 2 end fraction end cell row blank equals cell 0 times limit as x rightwards arrow infinity of fraction numerator begin display style 1 over x end style over denominator begin display style x over x end style plus begin display style 2 over x end style end fraction end cell row blank equals cell 0 times fraction numerator 0 over denominator 1 plus 0 end fraction end cell row blank equals cell 0 times 0 end cell row blank equals 0 end table$

Jadi, nilai dari $limit as x rightwards arrow infinity of fraction numerator sin left parenthesis 2 x minus 4 right parenthesis over denominator x squared minus 4 end fraction equals 0$ .