Pertanyaan

Tentukan nilai limit berikut. b. x → 0 lim tan 4 x − tan 6 x − sin 8 x sin 7 x + tan 5 x − sin 3 x

Tentukan nilai limit berikut.

b. $x \to 0 lim \frac{sin 7 x + tan 5 x - sin 3 x}{tan 4 x - tan 6 x - sin 8 x}$

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai $limit as x rightwards arrow 0 of fraction numerator sin 7 x plus tan 5 x minus sin 3 x over denominator tan 4 x minus tan 6 x minus sin 8 x end fraction$ adalah negative 9 over 10

Pembahasan

Dengan subtitusi langsung, Dengan mengubah bentuk fungsi trigonometri, Jadi, nilai adalah .

Dengan subtitusi langsung,

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin 7 x plus tan 5 x minus sin 3 x over denominator tan 4 x minus tan 6 x minus sin 8 x end fraction end cell equals cell fraction numerator sin 7 left parenthesis 0 right parenthesis plus tan 5 left parenthesis 0 right parenthesis minus sin 3 left parenthesis 0 right parenthesis over denominator tan 4 left parenthesis 0 right parenthesis minus tan 6 left parenthesis 0 right parenthesis minus sin 8 left parenthesis 0 right parenthesis end fraction end cell row blank equals cell fraction numerator sin left parenthesis 0 right parenthesis plus tan left parenthesis 0 right parenthesis minus sin left parenthesis 0 right parenthesis over denominator tan left parenthesis 0 right parenthesis minus tan left parenthesis 0 right parenthesis minus sin left parenthesis 0 right parenthesis end fraction end cell row blank equals cell 0 over 0 end cell end table$

Dengan mengubah bentuk fungsi trigonometri,

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator sin 7 x plus tan 5 x minus sin 3 x over denominator tan 4 x minus tan 6 x minus sin 8 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator sin 7 x plus tan 5 x minus sin 3 x over denominator tan 4 x minus tan 6 x minus sin 8 x end fraction cross times fraction numerator begin display style 1 over x end style over denominator begin display style 1 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator begin display style fraction numerator sin 7 x plus tan 5 x minus sin 3 x over denominator x end fraction end style over denominator begin display style fraction numerator tan 4 x minus tan 6 x minus sin 8 x over denominator x end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator begin display style fraction numerator sin 7 x over denominator x end fraction end style plus begin display style fraction numerator tan 5 x over denominator x end fraction end style minus begin display style fraction numerator sin 3 x over denominator x end fraction end style over denominator begin display style fraction numerator tan 4 x over denominator x end fraction end style minus begin display style fraction numerator tan 6 x over denominator x end fraction end style minus begin display style fraction numerator sin 8 x over denominator x end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style limit as x rightwards arrow 0 of fraction numerator sin 7 x over denominator x end fraction plus limit as x rightwards arrow 0 of fraction numerator tan 5 x over denominator x end fraction minus limit as x rightwards arrow 0 of fraction numerator sin 3 x over denominator x end fraction end style over denominator begin display style limit as x rightwards arrow 0 of fraction numerator tan 4 x over denominator x end fraction minus limit as x rightwards arrow 0 of fraction numerator tan 6 x over denominator x end fraction minus limit as x rightwards arrow 0 of fraction numerator sin 8 x over denominator x end fraction end style end fraction end cell row blank equals cell fraction numerator 7 plus 5 minus 3 over denominator 4 minus 6 minus 8 end fraction end cell row blank equals cell fraction numerator 9 over denominator negative 10 end fraction end cell row blank equals cell negative 9 over 10 end cell end table$

Jadi, nilai $limit as x rightwards arrow 0 of fraction numerator sin 7 x plus tan 5 x minus sin 3 x over denominator tan 4 x minus tan 6 x minus sin 8 x end fraction$ adalah negative 9 over 10 .