Pertanyaan

Jika f ( x ) = sin x cos 2 x maka nilai dari f ( 4 π )

Jika $f (x) = \frac{cos ^{2} x}{sin x}$ maka nilai dari $f (\frac{π}{4})$

R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Pembahasan

Diketahui : Ditanya :nilai dari ? Dijawab :

Diketahui : $begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator cos squared space straight x over denominator sin space straight x end fraction end style$

Ditanya : nilai dari ?

Dijawab :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight f open parentheses straight x close parentheses end cell equals cell fraction numerator cos squared straight x over denominator sin space straight x end fraction end cell row straight u equals cell cos squared straight x end cell row cell straight u apostrophe end cell equals cell 2 space cos space straight x times negative sin space straight x end cell row straight v equals cell sin space straight x end cell row cell straight v apostrophe end cell equals cell cos space straight x end cell row blank blank blank row cell straight f apostrophe open parentheses straight x close parentheses end cell equals cell straight u over straight v end cell row cell straight f apostrophe open parentheses straight x close parentheses end cell equals cell fraction numerator straight u apostrophe straight v minus uv apostrophe over denominator straight v squared end fraction end cell row blank equals cell fraction numerator negative 2 space cos space straight x times sin space straight x open parentheses sin space straight x close parentheses minus cos squared straight x open parentheses cos space straight x close parentheses over denominator sin squared space straight x end fraction end cell row cell straight f apostrophe open parentheses straight pi over 4 close parentheses end cell equals cell fraction numerator negative 2 space cos space open parentheses straight pi over 4 close parentheses times sin space open parentheses straight pi over 4 close parentheses open parentheses sin space open parentheses straight pi over 4 close parentheses close parentheses minus cos squared open parentheses straight pi over 4 close parentheses open parentheses cos space open parentheses straight pi over 4 close parentheses close parentheses over denominator sin squared space open parentheses straight pi over 4 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses negative up diagonal strike 2 times begin display style fraction numerator 1 over denominator up diagonal strike 2 end fraction end style square root of 2 times 1 half square root of 2 times 1 half square root of 2 close parentheses minus open parentheses 1 half square root of 2 times 1 half square root of 2 times 1 half square root of 2 close parentheses over denominator 1 half square root of 2 times 1 half square root of 2 end fraction end cell row blank equals cell fraction numerator begin display style 2 over 4 end style square root of 2 minus begin display style 4 over 8 end style square root of 2 over denominator begin display style 2 over 4 end style end fraction end cell row blank equals cell fraction numerator 0 over denominator 2 over 4 end fraction end cell row blank equals 0 end table end style$