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x→0lim​x tan xsin2 x−cos x+1​=...

Pertanyaan

begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator sin squared space x minus cos space x plus 1 over denominator x space tan space x end fraction equals... end style

  1. begin mathsize 12px style 3 over 2 end style

  2. begin mathsize 12px style 1 half end style

  3. begin mathsize 12px style negative 1 half end style

  4. -1

  5. -2

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Ingat!

begin mathsize 12px style cos space x equals 1 minus 2 space sin squared space 1 half x end style

 

maka:

begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator sin squared space x minus cos space x plus 1 over denominator x space tan space x end fraction  equals limit as x rightwards arrow 0 of fraction numerator begin display style sin squared space x minus open parentheses 1 minus 2 space sin squared space 1 half x close parentheses plus 1 end style over denominator begin display style x space tan space x end style end fraction  equals limit as x rightwards arrow 0 of fraction numerator begin display style sin squared space x minus 1 plus 2 space sin squared space 1 half x plus 1 end style over denominator begin display style x space tan space x end style end fraction  equals limit as x rightwards arrow 0 of fraction numerator begin display style sin squared space x plus 2 space sin squared space 1 half x end style over denominator begin display style x space tan space x end style end fraction  equals limit as x rightwards arrow 0 of open parentheses fraction numerator begin display style horizontal strike sin space x end strike space. space horizontal strike sin space x end strike end style over denominator horizontal strike x space tan space x end strike end fraction plus fraction numerator 2 space horizontal strike sin space begin display style 1 half end style horizontal strike x times horizontal strike sin space begin display style 1 half end style horizontal strike x over denominator horizontal strike x space tan space x end strike end fraction close parentheses  equals limit as x rightwards arrow 0 of open parentheses 1 plus 2 times 1 half times 1 half close parentheses  equals 1 plus 1 half  equals 3 over 2 end style

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