Tentukan nilai limit berikut. c. x→52lim(5x−2)210x−5

Pertanyaan

Tentukan nilai limit berikut.

c. $begin mathsize 14px style limit as x rightwards arrow 2 over 5 of fraction numerator 10 x minus 5 over denominator open parentheses 5 x minus 2 close parentheses squared end fraction end style$

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

nilai dari $limit as x rightwards arrow 2 over 5 of fraction numerator 10 x minus 5 over denominator open parentheses 5 x minus 2 close parentheses squared end fraction equals negative infinity$ .

Pembahasan

Untuk menyelesaikan soal tersebut kita substitusi nilai $x=\frac25$ pada limit fungsi tersebut diperoleh:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 over 5 of fraction numerator 10 x minus 5 over denominator blank end fraction end cell equals cell fraction numerator 10 open parentheses begin display style 2 over 5 end style close parentheses minus 5 over denominator open parentheses 5 open parentheses begin display style 2 over 5 end style close parentheses minus 2 close parentheses squared end fraction end cell row blank equals cell fraction numerator 4 minus 5 over denominator open parentheses 2 minus 2 close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 0 squared end fraction end cell row blank equals cell negative infinity end cell end table end style$

Dengan demikian, nilai dari $limit as x rightwards arrow 2 over 5 of fraction numerator 10 x minus 5 over denominator open parentheses 5 x minus 2 close parentheses squared end fraction equals negative infinity$ .