Nilai dari x→0lim​2x2cos 2x sin23x+cos23x−1​= ...

Pertanyaan

Nilai dari limit as x rightwards arrow 0 of fraction numerator cos space 2 x space sin squared 3 x plus cos squared 3 x minus 1 over denominator 2 x squared end fraction equals space... 

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

 limit as x rightwards arrow 0 of fraction numerator cos space 2 x space sin squared 3 x plus cos squared 3 x minus 1 over denominator 2 x squared end fraction equals space 9 over 4

Pembahasan

Dengan menggunakan rumus limit as x rightwards arrow 0 of fraction numerator sin space a x over denominator b x end fraction equals a over b dan limit as x rightwards arrow 0 of cos space a x equals 0, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator cos space 2 x space sin squared 3 x plus cos squared 3 x minus 1 over denominator 2 x squared end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator cos space 2 x space sin squared 3 x over denominator 2 x squared end fraction plus limit as x rightwards arrow 0 of fraction numerator cos squared 3 x minus 1 over denominator 2 x squared end fraction end cell row blank equals cell 1 half times limit as x rightwards arrow 0 of fraction numerator space sin squared 3 x over denominator x squared end fraction times limit as x rightwards arrow 0 of cos space 2 x plus limit as x rightwards arrow 0 of fraction numerator open parentheses 1 minus 2 sin squared open parentheses begin display style 3 over 2 end style x close parentheses close parentheses minus 1 over denominator 2 x squared end fraction end cell row blank equals cell 1 half times limit as x rightwards arrow 0 of fraction numerator space sin squared 3 x over denominator x squared end fraction times limit as x rightwards arrow 0 of cos space 2 x plus limit as x rightwards arrow 0 of fraction numerator negative 2 sin squared open parentheses begin display style 3 over 2 x end style close parentheses over denominator 2 x squared end fraction end cell row blank equals cell 1 half times limit as x rightwards arrow 0 of fraction numerator space sin squared 3 x over denominator x squared end fraction times limit as x rightwards arrow 0 of cos space 2 x minus limit as x rightwards arrow 0 of fraction numerator sin squared open parentheses begin display style 3 over 2 x end style close parentheses over denominator x squared end fraction end cell row blank equals cell 1 half times limit as x rightwards arrow 0 of open parentheses fraction numerator space sin 3 x over denominator x end fraction close parentheses squared times limit as x rightwards arrow 0 of cos space 2 x minus limit as x rightwards arrow 0 of open parentheses fraction numerator sin open parentheses begin display style 3 over 2 x end style close parentheses over denominator x end fraction close parentheses squared end cell row blank equals cell 1 half times open parentheses 3 over 1 close parentheses squared times 1 minus open parentheses fraction numerator begin display style 3 over 2 end style over denominator 1 end fraction close parentheses squared end cell row blank equals cell 9 over 2 minus 9 over 4 end cell row blank equals cell fraction numerator 18 minus 9 over denominator 4 end fraction end cell row blank equals cell 9 over 4 end cell end table  

Jadi, limit as x rightwards arrow 0 of fraction numerator cos space 2 x space sin squared 3 x plus cos squared 3 x minus 1 over denominator 2 x squared end fraction equals space 9 over 4

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