Pertanyaan

Hasi dari x → − ∞ lim ( x − 5 ) 3 ⋅ ( 2 x 2 + 4 ) 2 ( x 3 − 7 ) 2 ⋅ 3 27 x 3 − 16 x 2 + 4 adalah ....

Hasi dari $x \to - \infty lim \frac{( x ^{3} - 7 ) ^{2} \cdot 3 27 x ^{3} - 16 x ^{2} + 4}{( x - 5 ) ^{3} \cdot ( 2 x ^{2} + 4 ) ^{2}}$ adalah ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Misalkan x = - p sehingga p = - x , maka apabila x → - ∞ , didapat bahwa p → ∞ . Oleh karena itu, Jadi, jawaban yang tepat adalah C.

Misalkan x = - p sehingga p = - x , maka apabila x → - ∞ , didapat bahwa p → ∞ . Oleh karena itu,

$begin mathsize 14px style limit as x rightwards arrow negative straight infinity of invisible function application fraction numerator open parentheses x cubed minus 7 close parentheses squared times cube root of 27 x cubed minus 16 x squared plus 4 end root over denominator open parentheses x minus 5 close parentheses cubed times open parentheses 2 x squared plus 4 close parentheses squared end fraction equals limit as p rightwards arrow straight infinity of invisible function application fraction numerator open parentheses open parentheses negative p close parentheses cubed minus 7 close parentheses squared times cube root of 27 open parentheses negative p close parentheses cubed minus 16 open parentheses negative p close parentheses squared plus 4 end root over denominator open parentheses open parentheses negative p close parentheses minus 5 close parentheses cubed times open parentheses 2 open parentheses negative p close parentheses squared plus 4 close parentheses squared end fraction equals limit as p rightwards arrow straight infinity of invisible function application fraction numerator open parentheses negative p cubed minus 7 close parentheses squared times cube root of negative 27 p cubed minus 16 p squared plus 4 end root over denominator open parentheses negative p minus 5 close parentheses cubed times open parentheses 2 p squared plus 4 close parentheses squared end fraction equals limit as p rightwards arrow straight infinity of invisible function application fraction numerator open parentheses negative p cubed minus 7 close parentheses squared times cube root of negative 27 p cubed minus 16 p squared plus 4 end root over denominator open parentheses negative p minus 5 close parentheses cubed times open parentheses 2 p squared plus 4 close parentheses squared end fraction times fraction numerator 1 over p to the power of 7 over denominator 1 over p to the power of 7 end fraction equals limit as p rightwards arrow straight infinity of invisible function application fraction numerator open parentheses negative p cubed minus 7 close parentheses squared times cube root of negative 27 p cubed minus 16 p squared plus 4 end root over denominator open parentheses negative p minus 5 close parentheses cubed times open parentheses 2 p squared plus 4 close parentheses squared end fraction times fraction numerator 1 over p to the power of 6 times 1 over p over denominator 1 over p cubed times 1 over p to the power of 4 end fraction equals limit as p rightwards arrow straight infinity of invisible function application fraction numerator open parentheses negative p cubed minus 7 close parentheses squared times cube root of negative 27 p cubed minus 16 p squared plus 4 end root over denominator open parentheses negative p minus 5 close parentheses cubed times open parentheses 2 p squared plus 4 close parentheses squared end fraction times fraction numerator open parentheses 1 over p cubed close parentheses squared times cube root of 1 over p cubed end root over denominator open parentheses 1 over p close parentheses cubed times open parentheses 1 over p squared close parentheses squared end fraction equals limit as p rightwards arrow straight infinity of invisible function application fraction numerator open parentheses negative p cubed minus 7 close parentheses squared times open parentheses 1 over p cubed close parentheses squared times cube root of negative 27 p cubed minus 16 p squared plus 4 end root times cube root of 1 over p cubed end root over denominator open parentheses negative p minus 5 close parentheses cubed times open parentheses 1 over p close parentheses cubed times open parentheses 2 p squared plus 4 close parentheses squared times open parentheses 1 over p squared close parentheses squared end fraction equals limit as p rightwards arrow straight infinity of invisible function application fraction numerator open parentheses open parentheses negative p cubed minus 7 close parentheses bullet 1 over p cubed close parentheses squared times cube root of open parentheses negative 27 p cubed minus 16 p squared plus 4 close parentheses times 1 over p cubed end root over denominator open parentheses open parentheses negative p minus 5 close parentheses times 1 over p close parentheses cubed times open parentheses open parentheses 2 p squared plus 4 close parentheses times 1 over p squared close parentheses squared end fraction equals limit as p rightwards arrow straight infinity of invisible function application fraction numerator open parentheses negative 1 minus 7 over p cubed close parentheses squared times cube root of negative 27 minus 16 over p plus 4 over p cubed end root over denominator open parentheses negative 1 minus 5 over p close parentheses cubed times open parentheses 2 plus 4 over p squared close parentheses squared end fraction equals fraction numerator open parentheses negative 1 minus 0 close parentheses squared times cube root of negative 27 minus 0 plus 0 end root over denominator open parentheses negative 1 minus 0 close parentheses cubed times open parentheses 2 plus 0 close parentheses squared end fraction equals fraction numerator open parentheses negative 1 close parentheses squared times cube root of negative 27 end root over denominator open parentheses negative 1 close parentheses cubed times open parentheses 2 close parentheses squared end fraction equals fraction numerator 1 times open parentheses negative 3 close parentheses over denominator open parentheses negative 1 close parentheses times 4 end fraction equals 3 over 4 end style$

Jadi, jawaban yang tepat adalah C.