SMA

Nilai x→6lim​x−626​x​−12​ adala

Nilai begin mathsize 14px style limit as straight x rightwards arrow 6 of fraction numerator 2 square root of 6 square root of straight x minus 12 over denominator straight x minus 6 end fraction end style adalah …

A. begin mathsize 14px style 12 end style
B. begin mathsize 14px style 2 square root of 6 end style
C.begin mathsize 14px style space square root of 6 end style
D. begin mathsize 14px style 1 end style
E. begin mathsize 14px style 1 over 6 square root of 6 end style

Pembahasan

Dengan menggunakan metode mengalikan bentuk sekawan, maka :

table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow 6 of open parentheses fraction numerator 2 square root of 6 square root of x minus 12 over denominator x minus 6 end fraction close parentheses end cell equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 2 square root of 6 x end root minus 12 over denominator x minus 6 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 2 square root of 6 x end root minus 12 over denominator x minus 6 end fraction cross times fraction numerator 2 square root of 6 x end root plus 12 over denominator 2 square root of 6 x end root plus 12 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator open parentheses 2 square root of 6 x end root minus 12 close parentheses cross times open parentheses 2 square root of 6 x end root plus 12 close parentheses over denominator open parentheses x minus 6 close parentheses cross times open parentheses 2 square root of 6 x end root plus 12 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 4 open parentheses 6 x close parentheses minus 144 over denominator open parentheses x minus 6 close parentheses cross times open parentheses 2 square root of 6 x end root plus 12 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 24 x minus 144 over denominator open parentheses x minus 6 close parentheses cross times open parentheses 2 square root of 6 x end root plus 12 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 24 up diagonal strike open parentheses x minus 6 close parentheses end strike over denominator up diagonal strike open parentheses x minus 6 close parentheses end strike cross times open parentheses 2 square root of 6 x end root plus 12 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 24 over denominator open parentheses 2 square root of 6 x end root plus 12 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 6 of open parentheses fraction numerator 24 over denominator 2 open parentheses square root of 6 x end root plus 6 close parentheses end fraction close parentheses end cell row blank equals cell stack text lim end text with x rightwards arrow 6 below open parentheses fraction numerator 12 over denominator open parentheses square root of 6 x end root plus 6 close parentheses end fraction close parentheses end cell row blank equals cell fraction numerator 12 over denominator square root of 6 open parentheses 6 close parentheses end root plus 6 end fraction end cell row blank equals cell fraction numerator 12 over denominator 6 plus 6 end fraction end cell row blank equals 1 end table

Jadi, jawaban yang tepat adalah D.

 

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