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Hitunglah nilai dari x → ∞ lim ​ ( 4 x 2 + x ​ + 9 x 2 − x ​ − 5 x ) .

Hitunglah nilai dari .

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D. Enty

Master Teacher

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hasil limitnya adalah .

hasil limitnya adalah 1 over 12.

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Jadi, hasil limitnya adalah .

limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root plus square root of 9 x squared minus x end root minus 5 x close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root plus square root of 9 x squared minus x end root minus open parentheses 2 x plus 3 x close parentheses close parentheses limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root plus square root of 9 x squared minus x end root minus 5 x close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root plus square root of 9 x squared minus x end root minus 2 x minus 3 x close parentheses limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root plus square root of 9 x squared minus x end root minus 5 x close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root minus 2 x plus square root of 9 x squared minus x end root minus 3 x close parentheses limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root plus square root of 9 x squared minus x end root minus 5 x close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root minus square root of 4 x squared end root plus square root of 9 x squared minus x end root minus square root of 9 x squared end root close parentheses limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root plus square root of 9 x squared minus x end root minus 5 x close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root minus square root of 4 x squared end root close parentheses plus limit as x rightwards arrow infinity of open parentheses square root of 9 x squared minus x end root minus square root of 9 x squared end root close parentheses text Bentuk diatas sama dengan end text space limit as x rightwards arrow infinity of left parenthesis 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 space text dan karena end text space space a equals p space text maka nilai limitnya adalah end text space fraction numerator b minus q over denominator 2 square root of a end fraction comma space text sehingga end text limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root plus square root of 9 x squared minus x end root minus 5 x close parentheses equals fraction numerator 1 minus 0 over denominator 2 square root of 4 end fraction plus fraction numerator negative 1 minus 0 over denominator 2 square root of 9 end fraction limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root plus square root of 9 x squared minus x end root minus 5 x close parentheses equals 1 fourth minus 1 over 6 limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus x end root plus square root of 9 x squared minus x end root minus 5 x close parentheses equals fraction numerator 3 minus 2 over denominator 12 end fraction equals 1 over 12

Jadi, hasil limitnya adalah 1 over 12.

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