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Nilai dari .

Nilai dari limit as x rightwards arrow infinity of space open parentheses square root of 4 x squared minus 8 x plus 3 end root minus 2 x minus 4 close parentheses equals....

Jawaban:

Gunakan konsep limit tak hingga bentuk akar.

begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root close parentheses equals open curly brackets table attributes columnalign left end attributes row cell infinity comma space a greater than p end cell row cell fraction numerator b minus q over denominator 2 square root of a end fraction comma space a equals p end cell row cell negative infinity comma space a less than p end cell end table close end style 

Untuk menggunakan konsep di atas, harus diubah terlebih dahulu menjadi selisih bentuk akar.

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 2px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 3 end root minus 2 x minus 4 close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 3 end root minus open parentheses 2 x plus 4 close parentheses close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 3 end root minus square root of open parentheses 2 x plus 4 close parentheses squared end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 3 end root minus square root of 4 x squared plus 16 x plus 16 end root close parentheses end cell row blank equals cell fraction numerator b minus q over denominator 2 square root of a end fraction equals fraction numerator negative 8 minus 16 over denominator 2 square root of 4 end fraction end cell row blank equals cell fraction numerator negative 24 over denominator 4 end fraction end cell row blank equals cell negative 6 end cell end table

Jadi, diperoleh nilainya adalah limit as x rightwards arrow infinity of space open parentheses square root of 4 x squared minus 8 x plus 3 end root minus 2 x minus 4 close parentheses equals negative 6

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