Pertanyaan

x → 2 lim x 2 + 1 − 5 x − 2 = ....

$x \to 2 lim \frac{x - 2}{x ^{2} + 1 - 5} = ....$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

D. Enty

Master Teacher

Jawaban terverifikasi

Jawaban

.

$limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator square root of x squared plus 1 end root minus square root of 5 end fraction equals fraction numerator square root of 5 over denominator 2 end fraction$ .

Pembahasan

Menentukan limit dengan metode mengalikan dengan akar sekawan Jadi, .

Menentukan limit dengan metode mengalikan dengan akar sekawan

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator square root of x squared plus 1 end root minus square root of 5 end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator square root of x squared plus 1 end root minus square root of 5 end fraction times fraction numerator square root of x squared plus 1 end root plus square root of 5 over denominator square root of x squared plus 1 end root plus square root of 5 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x minus 2 close parentheses open parentheses square root of x squared plus 1 end root plus square root of 5 close parentheses over denominator open parentheses square root of x squared plus 1 end root minus square root of 5 close parentheses open parentheses square root of x squared plus 1 end root plus square root of 5 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x minus 2 close parentheses open parentheses square root of x squared plus 1 end root plus square root of 5 close parentheses over denominator x squared plus 1 minus 5 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x minus 2 close parentheses open parentheses square root of x squared plus 1 end root plus square root of 5 close parentheses over denominator x squared minus 4 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x minus 2 close parentheses open parentheses square root of x squared plus 1 end root plus square root of 5 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses x plus 2 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses square root of x squared plus 1 end root plus square root of 5 close parentheses over denominator open parentheses x plus 2 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses square root of 2 squared plus 1 end root plus square root of 5 close parentheses over denominator open parentheses 2 plus 2 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 5 plus square root of 5 over denominator 4 end fraction end cell row blank equals cell fraction numerator 2 square root of 5 over denominator 4 end fraction end cell row blank equals cell fraction numerator square root of 5 over denominator 2 end fraction end cell end table$

Jadi, $limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator square root of x squared plus 1 end root minus square root of 5 end fraction equals fraction numerator square root of 5 over denominator 2 end fraction$ .