Tentukan nilai limit dari fungsi-fungsi berikut ini: x→1lim2−x2+31−x2

Pertanyaan

Tentukan nilai limit dari fungsi-fungsi berikut ini:

$begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 1 minus x squared over denominator 2 minus square root of x squared plus 3 end root end fraction end style$

D. Enty

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari $begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 1 minus x squared over denominator 2 minus square root of x squared plus 3 end root end fraction end style$ adalah

Pembahasan

Dengan menggunakan metode mengalikan akar sekawan, maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator 1 minus x squared over denominator 2 minus square root of x squared plus 3 end root end fraction end cell equals cell limit as x rightwards arrow 1 of open parentheses fraction numerator 1 minus x squared over denominator 2 minus square root of x squared plus 3 end root end fraction times fraction numerator 2 plus square root of x squared plus 3 end root over denominator 2 plus square root of x squared plus 3 end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator open parentheses 1 minus x squared close parentheses open parentheses 2 plus square root of x squared plus 3 end root close parentheses over denominator open parentheses 2 minus square root of x squared plus 3 end root close parentheses open parentheses 2 plus square root of x squared plus 3 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator open parentheses 1 minus x squared close parentheses open parentheses 2 plus square root of x squared plus 3 end root close parentheses over denominator 4 minus open parentheses x squared plus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator open parentheses 1 minus x squared close parentheses open parentheses 2 plus square root of x squared plus 3 end root close parentheses over denominator 4 minus x squared minus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator down diagonal strike open parentheses 1 minus x squared close parentheses end strike open parentheses 2 plus square root of x squared plus 3 end root close parentheses over denominator down diagonal strike 1 minus x squared end strike end fraction end cell row blank equals cell limit as x rightwards arrow 1 of open parentheses 2 plus square root of x squared plus 3 end root close parentheses end cell row blank equals cell 2 plus square root of 1 squared plus 3 end root end cell row blank equals cell 2 plus square root of 1 plus 3 end root end cell row blank equals cell 2 plus square root of 4 end cell row blank equals cell 2 plus 2 end cell row blank equals 4 end table end style$

Jadi, nilai dari $begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 1 minus x squared over denominator 2 minus square root of x squared plus 3 end root end fraction end style$ adalah .