Pertanyaan

Tentukan nilai limit fungsi berikut. 4. x → 4 lim x 2 − 3 x − 4 x 2 + 5 x − 36

Tentukan nilai limit fungsi berikut.

$4. x \to 4 lim \frac{x ^{2} + 5 x - 36}{x ^{2} - 3 x - 4}$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari $begin mathsize 14px style limit as x rightwards arrow 4 of space fraction numerator x squared plus 5 x minus 36 over denominator x squared minus 3 x minus 4 end fraction equals 13 over 5 end style$ .

Pembahasan

Diketahui: Pembagian limit fungsi. Sederhanakan limit fungsi yang diketahui menggunakan metode pemfaktoran seperti berikut: Substitusi dengan pada limit fungsi yang telah disederhanakan seperti berikut: Jadi, nilai dari .

Diketahui:

Pembagian limit fungsi.

Sederhanakan limit fungsi yang diketahui menggunakan metode pemfaktoran seperti berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator x squared plus 5 x minus 36 over denominator x squared minus 3 x minus 4 end fraction end cell equals cell limit as x rightwards arrow 4 of space fraction numerator x squared plus 9 x minus 4 x minus 36 over denominator x squared plus x minus 4 x minus 4 end fraction end cell row blank equals cell limit as x rightwards arrow 4 of space fraction numerator x open parentheses x plus 9 close parentheses minus 4 open parentheses x plus 9 close parentheses over denominator x open parentheses x plus 1 close parentheses minus 4 open parentheses x plus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 4 of space fraction numerator open parentheses x plus 9 close parentheses down diagonal strike open parentheses x minus 4 close parentheses end strike over denominator open parentheses x plus 1 close parentheses down diagonal strike open parentheses x minus 4 close parentheses end strike end fraction end cell row blank equals cell limit as x rightwards arrow 4 of space fraction numerator x plus 9 over denominator x plus 1 end fraction end cell end table end style$

Substitusi begin mathsize 14px style x end style dengan begin mathsize 14px style 4 end style pada limit fungsi yang telah disederhanakan seperti berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator x plus 9 over denominator x plus 1 end fraction end cell equals cell fraction numerator 4 plus 9 over denominator 4 plus 1 end fraction end cell row blank equals cell 13 over 5 end cell end table end style$

Jadi, nilai dari $begin mathsize 14px style limit as x rightwards arrow 4 of space fraction numerator x squared plus 5 x minus 36 over denominator x squared minus 3 x minus 4 end fraction equals 13 over 5 end style$ .