SMA

Nilai x→4lim​x​−26xx​−24x​​ adalah …

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

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

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 48.

Jadi, jawaban yang tepat adalah D.

 

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