Pertanyaan

x → 1 lim x − 1 x − 2 x − 1 = ...

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

D. Entry

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari adalah .

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

Pembahasan

Dengan menerapkanpenyelesaian limit dengan metode mengalikan akar sekawan, diperoleh perhitungan sebagai berikut. Jadi, nilai dari adalah .

Dengan menerapkan penyelesaian limit dengan metode mengalikan akar sekawan, diperoleh perhitungan sebagai berikut.

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

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