Pertanyaan

Tentukan nilai limit fungsi berikut! a. x → 1 lim x 2 − 1 x − 1 dengan memisalkan x = t 2

Tentukan nilai limit fungsi berikut!

a. $x \to 1 lim \frac{x - 1}{x ^{2} - 1}$ dengan memisalkan $x = t^{2}$

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

nilai adalah

nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of x minus 1 over denominator x squared minus 1 end fraction end cell end table end style$ adalah

Pembahasan

Dengan memisalkan maka: Jadi,nilai adalah

Dengan memisalkan maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator square root of x minus 1 over denominator x squared minus 1 end fraction end cell equals cell limit as t squared rightwards arrow 1 of fraction numerator square root of t squared end root minus 1 over denominator open parentheses t squared close parentheses squared minus 1 end fraction end cell row blank equals cell limit as t squared rightwards arrow 1 of fraction numerator t minus 1 over denominator t to the power of 4 minus 1 end fraction end cell row blank equals cell limit as t squared rightwards arrow 1 of fraction numerator t minus 1 over denominator open parentheses t squared minus 1 close parentheses open parentheses t squared plus 1 close parentheses end fraction end cell row blank equals cell limit as t squared rightwards arrow 1 of fraction numerator t minus 1 over denominator left parenthesis t minus 1 right parenthesis left parenthesis t plus 1 right parenthesis open parentheses t squared plus 1 close parentheses end fraction end cell row blank equals cell limit as t squared rightwards arrow 1 of fraction numerator 1 over denominator left parenthesis t plus 1 right parenthesis open parentheses t squared plus 1 close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator open parentheses square root of 1 plus 1 close parentheses open parentheses 1 squared plus 1 close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 times 2 end fraction end cell row blank equals cell 1 fourth end cell end table end style$

Jadi,nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of x minus 1 over denominator x squared minus 1 end fraction end cell end table end style$ adalah

Latihan Bab

Konsep Kilat

Konsep Limit

Sifat Limit

Limit Fungsi Aljabar