NIlai dari x→1lim1−x22−4x sama dengan....

Pertanyaan

NIlai dari $begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 2 minus square root of 4 x end root over denominator 1 minus x squared end fraction end style$ sama dengan....

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Dengan menggunakan mdetode perkalian akar sekawan dan pemfaktoran diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator 2 minus square root of 4 x end root over denominator 1 minus x squared end fraction end cell equals cell limit as x rightwards arrow 1 of fraction numerator 2 minus square root of 4 x end root over denominator 1 minus x squared end fraction cross times fraction numerator 2 plus square root of 4 x end root over denominator 2 plus square root of 4 x end root end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 4 minus 4 x over denominator open parentheses 1 minus x squared close parentheses open parentheses 2 plus square root of 4 x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 4 open parentheses 1 minus x close parentheses over denominator open parentheses 1 minus x close parentheses open parentheses 1 plus x close parentheses open parentheses 2 plus square root of 4 x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 4 over denominator open parentheses 1 plus x close parentheses open parentheses 2 plus square root of 4 x end root close parentheses end fraction end cell row blank equals cell fraction numerator 4 over denominator open parentheses 1 plus 1 close parentheses open parentheses 2 plus square root of 4 times 1 end root close parentheses end fraction end cell row blank equals cell fraction numerator 4 over denominator 2 times open parentheses 2 plus 2 close parentheses end fraction end cell row blank equals cell 4 over 8 end cell row blank equals cell 1 half end cell end table$

Dengan demikian hasil dari $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 minus square root of 4 x end root over denominator 1 minus x squared end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table$ .

Oleh karena itu, jawaban yang benar adalah C.