Pertanyaan

Hasil dari x → 0 lim sin 3 x cos 9 x − sin 3 x cos 3 x sin 6 x − tan 6 x adalah ....

Hasil dari $x \to 0 lim \frac{sin 6 x - tan 6 x}{sin 3 x cos 9 x - sin 3 x cos 3 x}$ adalah ....

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat bahwa Oleh karena itu, didapat dan Jadi,jawaban yang tepat adalah C.

Ingat bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application alpha end cell equals cell fraction numerator sin invisible function application alpha over denominator cos invisible function application alpha end fraction end cell row cell cos invisible function application alpha end cell equals cell 1 minus 2 sin squared invisible function application open parentheses 1 half alpha close parentheses end cell row cell cos invisible function application alpha minus cos invisible function application beta end cell equals cell negative 2 sin invisible function application open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses sin invisible function application open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses end cell end table end style$

Oleh karena itu, didapat

dan

$begin mathsize 14px style limit as x rightwards arrow 0 of invisible function application fraction numerator sin invisible function application 6 x minus tan invisible function application 6 x over denominator sin invisible function application 3 x cos invisible function application 9 x minus sin invisible function application 3 x cos invisible function application 3 x end fraction equals limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 6 x cos invisible function application 6 x minus tan invisible function application 6 x over denominator sin invisible function application 3 x open parentheses cos invisible function application 9 x minus cos invisible function application 3 x close parentheses end fraction equals limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 6 x open parentheses cos invisible function application 6 x minus 1 close parentheses over denominator sin invisible function application 3 x open parentheses cos invisible function application 9 x minus cos invisible function application 3 x close parentheses end fraction equals limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 6 x open parentheses open parentheses 1 minus 2 sin squared invisible function application open parentheses 1 half times 6 x close parentheses close parentheses minus 1 close parentheses over denominator sin invisible function application 3 x open parentheses negative 2 sin invisible function application open parentheses fraction numerator 9 x plus 3 x over denominator 2 end fraction close parentheses sin invisible function application open parentheses fraction numerator 9 x minus 3 x over denominator 2 end fraction close parentheses close parentheses end fraction equals limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 6 x open parentheses open parentheses 1 minus 2 sin squared invisible function application 3 x close parentheses minus 1 close parentheses over denominator sin invisible function application 3 x open parentheses negative 2 sin invisible function application open parentheses fraction numerator 12 x over denominator 2 end fraction close parentheses sin invisible function application open parentheses fraction numerator 6 x over denominator 2 end fraction close parentheses close parentheses end fraction equals limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 6 x open parentheses negative 2 sin squared invisible function application 3 x close parentheses over denominator negative 2 sin invisible function application 3 x open parentheses sin invisible function application 6 x sin invisible function application 3 x close parentheses end fraction equals limit as x rightwards arrow 0 of invisible function application fraction numerator up diagonal strike negative 2 end strike tan invisible function application 6 x up diagonal strike sin squared invisible function application 3 x end strike over denominator up diagonal strike negative 2 end strike sin invisible function application 6 x up diagonal strike sin squared invisible function application 3 x end strike end fraction equals limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 6 x over denominator sin invisible function application 6 x end fraction equals limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator tan invisible function application 6 x over denominator sin invisible function application 6 x end fraction times fraction numerator 6 x over denominator 6 x end fraction close parentheses equals limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator tan invisible function application 6 x over denominator 6 x end fraction times fraction numerator 6 x over denominator sin invisible function application 6 x end fraction close parentheses equals 1 times 1 equals 1 end style$

Jadi, jawaban yang tepat adalah C.