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Hasil dari x → 0 lim ​ 4 − 4 cos 2 x tan 4 x sin x ​ adalah ....

Hasil dari  adalah ....

  1. begin mathsize 14px style negative 2 end style 

  2. begin mathsize 14px style negative 1 half end style 

  3. begin mathsize 14px style 1 end style 

  4. begin mathsize 14px style 1 half end style 

  5. begin mathsize 14px style 2 end style 

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa Jika disubstitusi , maka didapat Oleh karena itu, didapat Kemudian, didapat bahwa Jadi, jawaban yang tepat adalah D.

Perhatikan bahwa

begin mathsize 14px style cos invisible function application alpha equals 1 minus 2 sin squared invisible function application open parentheses 1 half alpha close parentheses end style              

Jika disubstitusi begin mathsize 14px style alpha equals 2 x end style, maka didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application 2 x end cell equals cell 1 minus 2 sin squared invisible function application open parentheses 1 half times 2 x close parentheses end cell row blank equals cell 1 minus 2 sin squared invisible function application x end cell end table end style             

Oleh karena itu, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 minus 4 cos invisible function application 2 x end cell equals cell 4 minus 4 open parentheses 1 minus 2 sin squared invisible function application x close parentheses end cell row blank equals cell 4 minus 4 plus 8 sin squared invisible function application x end cell row blank equals cell 8 sin squared invisible function application x end cell end table end style               

Kemudian, didapat bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 4 x sin invisible function application x over denominator 4 minus 4 cos invisible function application 2 x end fraction end cell equals cell limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 4 x sin invisible function application x over denominator 8 sin squared invisible function application x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 4 x up diagonal strike s i n invisible function application x end strike over denominator 8 sin invisible function application x up diagonal strike s i n invisible function application x end strike end fraction end cell row blank equals cell limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator tan invisible function application 4 x over denominator 8 sin invisible function application x end fraction times fraction numerator 4 x over denominator 4 x end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator tan invisible function application 4 x over denominator 4 x end fraction times fraction numerator x over denominator sin invisible function application x end fraction times 4 over 8 close parentheses end cell row blank equals cell 1 times 1 times 4 over 8 end cell row blank equals cell 1 half end cell end table end style                

Jadi, jawaban yang tepat adalah D.

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