x→2lim 12x+15x−1=. . .

Pertanyaan

$limit as x rightwards arrow 2 of space square root of fraction numerator 5 x minus 1 over denominator 12 x plus 1 end fraction end root equals$ . . .

$0,2$
$0,3$
$0,4$
$0,5$
$0,6$

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah E.

Ingat sifat limit

$\lim_{x\rightarrow a}\;x=a$
$\lim_{x\rightarrow a}\;k=k$
$\lim_{x\rightarrow a}\;kx=k.\lim_{x\rightarrow a}x$
$\lim_{x\rightarrow a}\;\left[f(x)-g(x)\right]=\lim_{x\rightarrow a}f(x)-\lim_{x\rightarrow a}g(x)$
$\lim_{x\rightarrow a}\;\left[f(x)+g(x)\right]=\lim_{x\rightarrow a}f(x)+\lim_{x\rightarrow a}g(x)$
$\lim_{x\rightarrow a}\;\left[f(x)\div g(x)\right]=\lim_{x\rightarrow a}f(x)\div\lim_{x\rightarrow a}g(x)$
$\lim_{x\rightarrow a}\;\left[f(x)\right]^n=\left[\lim_{x\rightarrow a}f(x)\right]^n$

Dengan menggunakan sifat-sifat di atas maka diperoleh perhitungan sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of space square root of fraction numerator 5 x minus 1 over denominator 12 x plus 1 end fraction end root end cell equals cell square root of limit as x rightwards arrow 2 of fraction numerator 5 x minus 1 over denominator 12 x plus 1 end fraction end root end cell row blank equals cell square root of fraction numerator limit as x rightwards arrow 2 of left parenthesis 5 x minus 1 right parenthesis over denominator limit as x rightwards arrow 2 of left parenthesis 12 x plus 1 right parenthesis end fraction end root end cell row blank equals cell square root of fraction numerator limit as x rightwards arrow 2 of 5 x minus limit as x rightwards arrow 2 of 1 over denominator limit as x rightwards arrow 2 of 12 x plus limit as x rightwards arrow 2 of 1 end fraction end root end cell row blank equals cell square root of fraction numerator 5 times limit as x rightwards arrow 2 of x minus limit as x rightwards arrow 2 of 1 over denominator 12 times stack lim space x with x rightwards arrow 2 below plus limit as x rightwards arrow 2 of 1 end fraction end root end cell row blank equals cell square root of fraction numerator left parenthesis 5 times 2 right parenthesis minus 1 over denominator left parenthesis 12 times 2 right parenthesis plus 1 end fraction end root end cell row blank equals cell square root of fraction numerator 10 minus 1 over denominator 24 plus 1 end fraction end root end cell row blank equals cell square root of 9 over 25 end root end cell row blank equals cell 3 over 5 end cell row blank equals cell 0 comma 6 end cell end table$

Oleh karena itu, jawaban yang benar adalah E.

5.0 (3 rating)

Pertanyaan serupa

x→5lim (x2−4x+4)2=. . .

5.0

Jawaban terverifikasi

Diberikan x→alimf(x)=3 dan x→alimg(x)=−1. Hitunglah nilai setiap limit berikut. a. x→alimf2(x)+g2(x) b. x→alimf(x)+g(x)2f(x)−3g(x) c. x→alim3g(x)[f(x)+3] d. x→alim[f(x)−3]4

4.8

Jawaban terverifikasi

Nilai dari x→2lim 2x2+3x+16x2−7x−5 adalah...

0.0

Jawaban terverifikasi

x→4lim (x2−2x+1)=. . .

4.2

Jawaban terverifikasi

x→−2lim x+3x2−5x+4=...

0.0

Jawaban terverifikasi