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Tentukan nilai dari!

Tentukan nilai darilimit as x rightwards arrow straight pi over 4 of fraction numerator cos space 2 x over denominator cos space x minus sin space x end fraction!

Jawaban:

 table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight pi over 4 of fraction numerator cos space 2 x over denominator cos space x minus sin space x end fraction end cell equals cell limit as x rightwards arrow straight pi over 4 of fraction numerator cos squared x minus sin squared x over denominator cos x minus sin x end fraction end cell row blank equals cell limit as x rightwards arrow straight pi over 4 of fraction numerator up diagonal strike open parentheses cos space x minus sin space x close parentheses end strike open parentheses cos space x plus sin space x close parentheses over denominator up diagonal strike open parentheses cos space x minus sin space x close parentheses end strike end fraction end cell row blank equals cell cos space straight pi over 4 plus sin space straight pi over 4 end cell row blank equals cell 1 half square root of 2 plus 1 half square root of 2 end cell row blank equals cell square root of 2 end cell end table 

Jadi, nilai dari limit as x rightwards arrow straight pi over 4 of fraction numerator cos space 2 x over denominator cos space x minus sin space x end fraction adalah square root of 2

 

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