Tentukan nilai limit fungsi berikut. 10.x→5limx2−25x3−125

Pertanyaan

Tentukan nilai limit fungsi berikut.

$\style{font-size:14px}{10.\;\lim_{x\rightarrow5}\;\frac{x^3-125}{x^2-25}}$

Pembahasan Soal:

Diketahui:

Pembagian limit fungsi.

Sederhanakan limit fungsi yang diketahui menggunakan metode pemfaktoran seperti berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 5 of space fraction numerator x cubed minus 125 over denominator x squared minus 25 end fraction end cell equals cell limit as x rightwards arrow 5 of space fraction numerator open parentheses x minus 5 close parentheses open parentheses x squared plus 5 x plus 25 close parentheses over denominator x squared minus 25 end fraction end cell row blank equals cell limit as x rightwards arrow 5 of space fraction numerator down diagonal strike open parentheses x minus 5 close parentheses end strike open parentheses x squared plus 5 x plus 25 close parentheses over denominator down diagonal strike open parentheses x minus 5 close parentheses end strike open parentheses x plus 5 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 5 of space fraction numerator x squared plus 5 x plus 25 over denominator x plus 5 end fraction end cell end table end style$

Substitusi $begin mathsize 14px style x end style$ dengan $begin mathsize 14px style 5 end style$ pada limit fungsi yang telah disederhanakan seperti berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 5 of space fraction numerator x squared plus 5 x plus 25 over denominator x plus 5 end fraction end cell equals cell fraction numerator 5 squared plus 5 open parentheses 5 close parentheses plus 25 over denominator 5 plus 5 end fraction end cell row blank equals cell fraction numerator 25 plus 25 plus 25 over denominator 10 end fraction end cell row blank equals cell 75 over 10 end cell row blank equals cell 15 over 2 end cell end table end style$

Maka, nilai dari $begin mathsize 14px style limit as x rightwards arrow 5 of space fraction numerator x cubed minus 125 over denominator x squared minus 25 end fraction equals 15 over 2 end style$ .

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Ayu

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Terakhir diupdate 06 Oktober 2021