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Nilai dari adalah ....

Nilai dari $begin mathsize 14px style limit as x rightwards arrow straight infinity of invisible function application fraction numerator 2 x to the power of 4 minus 1 over denominator x cubed csc invisible function application open parentheses 1 over x close parentheses end fraction end style$ adalah ....

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H. Nufus

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Perhatikan bahwa Misalkan , maka .Ketika , maka , Sehingga

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$begin mathsize 14px style limit as x rightwards arrow straight infinity of invisible function application fraction numerator 2 x to the power of 4 minus 1 over denominator x cubed csc invisible function application open parentheses 1 over x close parentheses end fraction equals limit as x rightwards arrow straight infinity of invisible function application fraction numerator 2 x to the power of 4 minus 1 over denominator x cubed times fraction numerator 1 over denominator sin invisible function application open parentheses 1 over x close parentheses end fraction end fraction equals limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator 2 x to the power of 4 minus 1 over denominator x cubed end fraction times sin invisible function application open parentheses 1 over x close parentheses close parentheses equals limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator 2 x to the power of 4 minus 1 over denominator x cubed end fraction times x over x times sin invisible function application open parentheses 1 over x close parentheses close parentheses equals limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator 2 x to the power of 4 minus 1 over denominator x to the power of 4 end fraction times x times sin invisible function application open parentheses 1 over x close parentheses close parentheses equals limit as x rightwards arrow straight infinity of invisible function application fraction numerator 2 x to the power of 4 minus 1 over denominator x to the power of 4 end fraction times limit as x rightwards arrow straight infinity of invisible function application open parentheses x times sin invisible function application open parentheses 1 over x close parentheses close parentheses equals limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator 2 x to the power of 4 minus 1 over denominator x to the power of 4 end fraction times fraction numerator 1 over x to the power of 4 over denominator 1 over x to the power of 4 end fraction close parentheses times limit as x rightwards arrow straight infinity of invisible function application open parentheses x times sin invisible function application open parentheses 1 over x close parentheses close parentheses equals limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator 2 minus 1 over x to the power of 4 over denominator 1 end fraction close parentheses times limit as x rightwards arrow straight infinity of invisible function application open parentheses x times sin invisible function application open parentheses 1 over x close parentheses close parentheses equals fraction numerator 2 minus 0 over denominator 1 end fraction times limit as x rightwards arrow straight infinity of invisible function application open parentheses x times sin invisible function application open parentheses 1 over x close parentheses close parentheses equals 2 times limit as x rightwards arrow straight infinity of invisible function application open parentheses x times sin invisible function application open parentheses 1 over x close parentheses close parentheses end style$

Misalkan , maka .Ketika , maka , Sehingga

$begin mathsize 14px style 2 times limit as x rightwards arrow straight infinity of invisible function application open parentheses x times sin invisible function application open parentheses 1 over x close parentheses close parentheses equals 2 times limit as y rightwards arrow 0 of invisible function application open parentheses 1 over y times sin invisible function application y close parentheses equals 2 times limit as y rightwards arrow 0 of invisible function application fraction numerator sin invisible function application y over denominator y end fraction equals 2 times 1 equals 2 end style$