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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. dengan memisalkan

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M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

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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 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table end style 

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Pembahasan

Dengan memisalkan maka: Jadi,nilai adalah

Dengan memisalkan begin mathsize 14px style x equals t squared end style 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 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table end style 

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Konsep Limit

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