Pertanyaan

Nilai dari x → 4 π lim cos 2 2 x 1 − 2 sin 2 x adalah ...

Nilai dari $x \to \frac{π}{4} lim \frac{1 - 2 sin 2 x}{cos ^{2} 2 x}$ adalah ...

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Jawaban terverifikasi

Jawaban

limitnya adalah .

Pembahasan

Jadi, limitnya adalah .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight pi over 4 of space fraction numerator 1 minus sin space 2 x over denominator cos squared space 2 x end fraction end cell equals cell limit as x rightwards arrow straight pi over 4 of space fraction numerator 1 minus sin space 2 x over denominator 1 minus sin squared space 2 x space end fraction end cell row blank equals cell limit as x rightwards arrow straight pi over 4 of space fraction numerator 1 minus sin space 2 x over denominator open parentheses 1 minus sin space 2 x close parentheses open parentheses 1 plus sin space 2 x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow straight pi over 4 of space fraction numerator 1 over denominator open parentheses 1 plus sin space 2 x close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator open parentheses 1 plus sin space 2 open parentheses straight pi over 4 close parentheses close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator 1 plus sin space 90 degree end fraction end cell row blank equals cell 1 half end cell end table end style$

Jadi, limitnya adalah .