Pertanyaan

Misalkan . Maka nilai dari ..

Misalkan . Maka nilai dari $begin mathsize 14px style limit as h rightwards arrow 0 of invisible function application fraction numerator f open parentheses 2 plus h close parentheses minus f open parentheses 2 close parentheses over denominator h end fraction equals end style$ ..

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Jawaban terverifikasi

Pembahasan

Maka, jawaban yang tepat adalah D.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as h rightwards arrow 0 of invisible function application fraction numerator f open parentheses 2 plus h close parentheses minus f open parentheses 2 close parentheses over denominator h end fraction end cell equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator square root of 9 open parentheses 2 plus h close parentheses plus 1 end root minus square root of 9 open parentheses 2 close parentheses plus 1 end root over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator square root of 19 plus 9 h end root minus square root of 19 over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator square root of 19 plus 9 h end root minus square root of 19 over denominator h end fraction times fraction numerator square root of 19 plus 9 h end root plus square root of 19 over denominator square root of 19 plus 9 h end root plus square root of 19 end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses 19 plus 9 h close parentheses minus 19 over denominator h open parentheses square root of 19 plus 9 h end root plus square root of 19 close parentheses end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator 9 h over denominator h open parentheses square root of 19 plus 9 h end root plus square root of 19 close parentheses end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator 9 over denominator square root of 19 plus 9 h end root plus square root of 19 end fraction end cell row blank equals cell fraction numerator 9 over denominator square root of 19 plus 9 open parentheses 0 close parentheses end root plus square root of 19 end fraction end cell row blank equals cell fraction numerator 9 over denominator 2 square root of 19 end fraction end cell row blank equals cell 9 over 38 square root of 19 end cell end table end style$

Maka, jawaban yang tepat adalah D.