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Tentukan nilai dari

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator cos open parentheses 6 x close parentheses minus 1 over denominator 2 x times open parentheses tan open parentheses 9 x close parentheses close parentheses end fraction end style

N. Puspita

Master Teacher

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Pembahasan

Dengan menggunakan konsep limit trigonometri menuju space 0 dan identitas trigonometri. Maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator cos open parentheses 6 x close parentheses minus 1 over denominator 2 x times open parentheses tan open parentheses 9 x close parentheses close parentheses end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator negative 2 sin squared open parentheses 3 x close parentheses over denominator 2 x times open parentheses tan open parentheses 9 x close parentheses close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator negative sin open parentheses 3 x close parentheses times sin open parentheses 3 x close parentheses over denominator x times open parentheses tan open parentheses 9 x close parentheses close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator negative sin open parentheses 3 x close parentheses over denominator x end fraction times limit as x rightwards arrow 0 of fraction numerator sin open parentheses 3 x close parentheses over denominator tan open parentheses 9 x close parentheses end fraction end cell row blank equals cell negative 3 times 3 over 9 end cell row blank equals cell fraction numerator negative 9 over denominator 9 end fraction end cell row blank equals cell negative 1 end cell end table

Dengan  demikian nilai dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator cos open parentheses 6 x close parentheses minus 1 over denominator 2 x times open parentheses tan open parentheses 9 x close parentheses close parentheses end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table.

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