Roboguru

Hitunglah tiap limit fungsi berikut!

Hitunglah tiap limit fungsi berikut!

begin mathsize 14px style limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator 1 minus square root of x minus 3 end root end fraction end style  undefined 

  1. ... undefined 

  2. ... undefined 

Jawaban:

Gunakan akar sekawan untuk mengerjakan soal berikut
Akar sekawan dari begin mathsize 14px style 1 minus square root of x minus 3 end root end style adalah begin mathsize 14px style 1 plus square root of italic x minus sign 3 end root end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator 1 minus square root of x minus 3 end root end fraction end cell equals cell limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator 1 minus square root of x minus 3 end root end fraction cross times fraction numerator 1 plus square root of x minus 3 end root over denominator 1 plus square root of x minus 3 end root end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator left parenthesis x squared minus 16 right parenthesis left parenthesis 1 plus square root of x minus 3 end root right parenthesis over denominator 1 minus square root of x minus 3 end root plus square root of x minus 3 end root minus left parenthesis x minus 3 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator left parenthesis x squared minus 16 right parenthesis left parenthesis 1 plus square root of x minus 3 end root right parenthesis over denominator 1 minus x plus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator left parenthesis negative x plus 4 right parenthesis left parenthesis negative x plus 4 right parenthesis left parenthesis 1 plus square root of x minus 3 end root right parenthesis over denominator negative x plus 4 end fraction end cell row blank equals cell limit as x rightwards arrow 4 of left parenthesis negative x plus 4 right parenthesis left parenthesis 1 plus square root of x minus 3 end root right parenthesis end cell row blank equals cell open parentheses negative 4 plus 4 close parentheses open parentheses 1 plus square root of 4 minus 3 end root close parentheses end cell row blank equals cell open parentheses 0 close parentheses open parentheses 1 plus square root of 1 close parentheses end cell row blank equals 0 end table end style 

Jadi, hasil begin mathsize 14px style limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator 1 minus square root of x minus 3 end root end fraction equals 0 end style  

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