Pertanyaan

Nilai dari x → 4 π lim sin x + cos x sin 2 x adalah ...

Nilai dari $x \to \frac{π}{4} lim \frac{sin 2 x}{sin x + cos x}$ adalah ...

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

hasil dari .

hasil dari $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow straight pi over 4 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 2 x over denominator sin space x plus cos space x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 end cell end table$ .

Pembahasan

Mencari nilai dari : Jadi, hasil dari .

Mencari nilai dari $limit as x rightwards arrow straight pi over 4 of fraction numerator sin space 2 x over denominator sin space x plus cos space x end fraction$ :

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight pi over 4 of fraction numerator sin space 2 x over denominator sin space x plus cos space x end fraction end cell equals cell limit as x rightwards arrow thin space 45 to the power of ring operator thin space end exponent of open parentheses fraction numerator sin open parentheses 2 x close parentheses over denominator sin open parentheses x close parentheses plus cos open parentheses x close parentheses end fraction close parentheses end cell row blank equals cell fraction numerator sin open parentheses 2 times 45 degree close parentheses over denominator sin open parentheses 45 degree close parentheses plus cos open parentheses 45 degree close parentheses end fraction end cell row blank equals cell fraction numerator sin open parentheses 90 degree close parentheses over denominator sin open parentheses 45 degree close parentheses plus cos open parentheses 45 degree close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style 1 half square root of 2 plus 1 half square root of 2 end style end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell 1 half square root of 2 end cell end table$

Jadi, hasil dari $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow straight pi over 4 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 2 x over denominator sin space x plus cos space x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 end cell end table$ .