SMA

Nilai x→4limx−26xx−24x adalah …

AdministratorMarch 1, 2022

0 105 Less than a minute

Nilai $begin mathsize 14px style limit as straight x rightwards arrow 4 of fraction numerator 6 straight x square root of straight x minus 24 square root of straight x over denominator square root of straight x minus 2 end fraction end style$ adalah …

A. 12
B. 24
C. 36
D. 48
E. 64

Pembahasan

$table attributes columnalign right center left columnspacing 2px end attributes row cell limit as straight x rightwards arrow 4 of open parentheses fraction numerator 6 straight x square root of straight x minus 24 square root of straight x over denominator square root of straight x minus 2 end fraction close parentheses end cell equals cell limit as straight x rightwards arrow 4 of open parentheses fraction numerator 6 straight x square root of straight x minus 24 square root of straight x over denominator square root of straight x minus 2 end fraction close parentheses cross times open parentheses fraction numerator square root of x plus 2 over denominator square root of x plus 2 end fraction close parentheses end cell row cell ingat space bahwa space end cell cell open parentheses square root of a minus b close parentheses end cell cell open parentheses square root of a plus b close parentheses equals a minus b squared comma space maka end cell row cell limit as straight x rightwards arrow 4 of open parentheses fraction numerator 6 square root of straight x open parentheses straight x minus 4 close parentheses over denominator square root of straight x minus 2 end fraction close parentheses end cell equals cell limit as straight x rightwards arrow 4 of open parentheses fraction numerator open parentheses 6 straight x square root of straight x minus 24 square root of straight x close parentheses open parentheses square root of straight x plus 2 close parentheses over denominator x minus 4 end fraction close parentheses end cell row blank equals cell limit as straight x rightwards arrow 4 of open parentheses fraction numerator open parentheses 6 square root of straight x open parentheses straight x minus 4 close parentheses close parentheses open parentheses square root of straight x plus 2 close parentheses over denominator x minus 4 end fraction close parentheses end cell row blank equals cell limit as straight x rightwards arrow 4 of open parentheses 6 square root of x open parentheses square root of straight x plus 2 close parentheses close parentheses end cell row blank equals cell 6 square root of 4 open parentheses square root of 4 plus 2 close parentheses end cell row blank equals cell 6 times 2 open parentheses 2 plus 2 close parentheses end cell row blank equals cell 12 open parentheses 4 close parentheses end cell row blank equals 48 end table$

Jadi, jawaban yang tepat adalah D.