Pertanyaan

Nilai x → 3 lim x 2 + 2 x − 15 x 2 + 7 − 4 x + 4 = ....

Nilai $x \to 3 lim \frac{x ^{2} + 7 - 4 x + 4}{x ^{2} + 2 x - 15} = ....$

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Jadi, jawaban yang tepat adalah B.

$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 square root of x squared plus 7 end root minus square root of 4 x plus 4 end root over denominator x squared plus 2 x minus 15 end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses square root of x squared plus 7 end root minus square root of 4 x plus 4 end root close parentheses open parentheses square root of x squared plus 7 end root plus square root of 4 x plus 4 end root close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 3 close parentheses open parentheses square root of x squared plus 7 end root plus square root of 4 x plus 4 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 3 close parentheses open parentheses x minus 1 close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 3 close parentheses open parentheses square root of x squared plus 7 end root plus square root of 4 x plus 4 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 1 close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses square root of x squared plus 7 end root plus square root of 4 x plus 4 end root close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 3 minus 1 close parentheses over denominator open parentheses 3 plus 5 close parentheses open parentheses square root of 9 plus 7 end root plus square root of 12 plus 4 end root close parentheses end fraction end cell row blank equals cell fraction numerator 2 over denominator 8 open parentheses 2 square root of 16 close parentheses end fraction end cell row blank equals cell 1 over 32 end cell row blank blank blank end table end style$

Jadi, jawaban yang tepat adalah B.

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