Pertanyaan

x → 0 lim 2 x 4 cos x sin 2 x − 1 + cos 2 x = ...

$x \to 0 lim \frac{cos x sin ^{2} x - 1 + cos ^{2} x}{2 x ^{4}} = ...$

-1
1
4

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N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

Jawaban terverifikasi

Pembahasan

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow 0 of space fraction numerator cos space straight x space sin squared space straight x minus 1 plus cos squared space straight x over denominator 2 straight x to the power of 4 end fraction end cell equals cell limit as straight x rightwards arrow 0 of space fraction numerator cos space straight x space sin squared space straight x minus sin squared space straight x over denominator 2 straight x to the power of 4 end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of space fraction numerator sin squared space straight x space open parentheses cos space straight x space minus 1 close parentheses over denominator 2 straight x to the power of 4 end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of space fraction numerator sin squared space straight x space open parentheses negative 2 sin squared space begin display style 1 half end style straight x space close parentheses over denominator 2 straight x to the power of 4 end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of space fraction numerator sin squared space straight x space over denominator x squared end fraction fraction numerator open parentheses negative 2 sin squared space 1 half straight x space close parentheses over denominator 2 straight x squared end fraction end cell row blank equals cell 1 times negative 1 open parentheses 1 squared over 2 close parentheses end cell row blank equals cell negative 1 fourth end cell end table$