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x → 0 lim ​ x 2 cos 2 x sin 2 2 x ​ = …

   

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N. Puspita

Master Teacher

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 limit as x rightwards arrow 0 of space fraction numerator sin squared space 2 x over denominator x squared space cos space 2 x end fraction equals 4.

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Hasilnya didapatkan: Jadi, .

Hasilnya didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of space fraction numerator sin squared space 2 x over denominator x squared space cos space 2 x end fraction end cell equals cell limit as x rightwards arrow 0 of space fraction numerator sin space 2 x times sin space 2 x over denominator x squared space cos space 2 x end fraction times fraction numerator 4 x squared over denominator 4 x squared end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator sin space 2 x times sin space 2 x over denominator x squared space cos space 2 x end fraction times fraction numerator 4 x squared over denominator 2 x times 2 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator sin space 2 x over denominator 2 x end fraction times fraction numerator sin space 2 x over denominator 2 x end fraction times fraction numerator 4 x squared over denominator x squared end fraction times fraction numerator 1 over denominator cos space 2 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator sin space 2 x over denominator 2 x end fraction times limit as x rightwards arrow 0 of space fraction numerator sin space 2 x over denominator 2 x end fraction times limit as x rightwards arrow 0 of space fraction numerator 4 x squared over denominator x squared end fraction times limit as x rightwards arrow 0 of space fraction numerator 1 over denominator cos space 2 x end fraction end cell row blank equals cell 1 times 1 times 4 times 1 over 1 end cell row blank equals 4 end table 

Jadi, limit as x rightwards arrow 0 of space fraction numerator sin squared space 2 x over denominator x squared space cos space 2 x end fraction equals 4.

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