Pertanyaan

Diketahui f ( x ) = x 4 − a 4 x 2 − a 2 , a  = 0 . Nilai x → a lim f ( x ) = ....

Diketahui $f (x) = \frac{x ^{2} - a ^{2}}{x ^{4} - a ^{4}}, a \neq = 0$ . Nilai $x \to a lim f (x) =$ ....

$begin mathsize 14px style fraction numerator 1 over denominator 2 a squared end fraction end style$
$begin mathsize 14px style fraction numerator 1 over denominator 3 a squared end fraction end style$
$begin mathsize 14px style fraction numerator 1 over denominator 4 a squared end fraction end style$
$begin mathsize 14px style fraction numerator 1 over denominator 6 a squared end fraction end style$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Diketahui , maka nilai limitnya sebagai berikut. lim x → a f ( x ) = = = lim x → a x 4 − a 4 x 2 − a 2 a 4 − a 4 a 2 − a 2 0 0 Karena diperoleh nilai 0 0 , maka kerjakan dengan metode pemfaktoran. Oleh karena itu, jawaban yang tepat adalah B.

Diketahui $begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator x squared minus a squared over denominator x to the power of 4 minus a to the power of 4 end fraction comma space a not equal to 0 end style$ , maka nilai limitnya sebagai berikut.

$lim_{x \to a} f (x) = = = lim_{x \to a} \frac{x ^{2} - a ^{2}}{x ^{4} - a ^{4}} \frac{a ^{2} - a ^{2}}{a ^{4} - a ^{4}} \frac{0}{0}$

Karena diperoleh nilai $\frac{0}{0}$ , maka kerjakan dengan metode pemfaktoran.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a of f open parentheses x close parentheses end cell equals cell limit as x rightwards arrow a of fraction numerator x squared minus a squared over denominator x to the power of 4 minus a to the power of 4 end fraction end cell row blank equals cell limit as x rightwards arrow a of fraction numerator x squared minus a squared over denominator open parentheses x squared minus a squared close parentheses open parentheses x squared plus a squared close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow a of fraction numerator up diagonal strike x squared minus a squared end strike over denominator up diagonal strike open parentheses x squared minus a squared close parentheses end strike open parentheses x squared plus a squared close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow a of fraction numerator 1 over denominator x squared plus a squared end fraction end cell row blank equals cell fraction numerator 1 over denominator a squared plus a squared end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 a squared end fraction end cell end table end style$

Oleh karena itu, jawaban yang tepat adalah B.

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