Pertanyaan

Tentukannilai limit berikut! x → 1 lim x 4 − 1 x 3 − 1

Tentukan nilai limit berikut!

$x \to 1 lim \frac{x ^{3} - 1}{x ^{4} - 1}$

S. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai dari x → 1 lim x 4 − 1 x 3 − 1 = 4 3 .

nilai dari

x \to 1 lim \frac{x ^{3} - 1}{x ^{4} - 1} = \frac{3}{4}

Pembahasan

Dengan demikian, nilai dari x → 1 lim x 4 − 1 x 3 − 1 = 4 3 .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator x cubed minus 1 over denominator x to the power of 4 minus 1 end fraction end cell equals cell limit as x rightwards arrow 1 of fraction numerator open parentheses x minus 1 close parentheses open parentheses x squared plus x plus 1 close parentheses over denominator open parentheses x squared plus 1 close parentheses open parentheses x squared minus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator open parentheses x minus 1 close parentheses open parentheses x squared plus x plus 1 close parentheses over denominator open parentheses x squared plus 1 close parentheses open parentheses x minus 1 close parentheses open parentheses x plus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator x squared plus x plus 1 over denominator open parentheses x squared plus 1 close parentheses open parentheses x plus 1 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 1 squared plus 1 plus 1 close parentheses over denominator open parentheses 1 squared plus 1 close parentheses open parentheses 1 plus 1 close parentheses end fraction end cell row blank equals cell 3 over 4 end cell end table end style$

Dengan demikian, nilai dari $x \to 1 lim \frac{x ^{3} - 1}{x ^{4} - 1} = \frac{3}{4}$ .

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

4.7 (16 rating)

Pertanyaan serupa

Diketahui x → 1 lim x − 1 f ( x ) = − 2 dan x → 3 lim x − 3 f ( x ) = 10 .Jika f ( x ) merupakan fungsi berderajat 3 yang memenuhi kedua limittersebut, tentukanlah rumus fungsi .

4.8

Jawaban terverifikasi

NIlai dari x → 1 lim 1 − x 2 2 − 4 x sama dengan....

0.0

Jawaban terverifikasi

x → 4 lim x 2 − 2 x − 8 x 4 − 20 x 2 + 64 = ...

5.0

Jawaban terverifikasi

x → − 6 lim x + 6 x 2 − 36 = ...

4.7

Jawaban terverifikasi

x → 3 lim x − 3 x 2 − 7 x + 12 = ...