Diketahui f(x)=x4−a4x2−a2,a=0. Nilai x→alimf(x)...

Pertanyaan

Diketahui $f left parenthesis x right parenthesis equals fraction numerator x squared minus a squared over denominator x to the power of 4 minus a to the power of 4 end fraction comma space a not equal to 0$ . Nilai $\lim_{x\rightarrow a}f(x)=$

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

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

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

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

Oleh karena itu, jawaban yang tepat adalah B.