Roboguru

Hitunglah limit fungsi berikut.

Hitunglah limit fungsi berikut.

begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 2 close parentheses squared minus 1 over denominator x minus 3 end fraction end style  undefined 

  1. ... undefined 

  2. ... undefined 

Jawaban:

Dalam hal ini undefined dimanipulasi dengan cara faktorisasi yaitu dengan menguraikan suatu fungsi dengan cara difaktorkan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 2 close parentheses squared minus 1 over denominator x minus 3 end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator x squared minus 4 x plus 4 minus 1 over denominator x minus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator x squared minus 4 x plus 3 over denominator x minus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis x minus 1 right parenthesis over denominator x minus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of x minus 1 end cell row blank equals cell 3 minus 1 equals 2 end cell end table end style 

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 2 close parentheses squared minus 1 over denominator x minus 3 end fraction equals 2 end style 

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