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Nilai dari $begin mathsize 14px style limit as x rightwards arrow straight infinity of invisible function application fraction numerator open parentheses 1 minus 2 x squared close parentheses cot squared invisible function application open parentheses 1 over x close parentheses over denominator 3 x to the power of 4 end fraction end style$ adalah ...

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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 open parentheses 1 minus 2 x squared close parentheses cot squared invisible function application open parentheses 1 over x close parentheses over denominator 3 x to the power of 4 end fraction equals limit as x rightwards arrow straight infinity of invisible function application fraction numerator open parentheses 1 minus 2 x squared close parentheses times fraction numerator 1 over denominator tan squared invisible function application open parentheses 1 over x close parentheses end fraction over denominator 3 x to the power of 4 end fraction equals limit as x rightwards arrow straight infinity of invisible function application fraction numerator open parentheses 1 minus 2 x squared close parentheses times fraction numerator 1 over denominator tan squared invisible function application open parentheses 1 over x close parentheses end fraction over denominator 3 x to the power of 4 end fraction equals limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator 1 minus 2 x squared over denominator 3 x to the power of 4 end fraction times fraction numerator 1 over denominator tan squared invisible function application open parentheses 1 over x close parentheses end fraction close parentheses equals limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator 1 minus 2 x squared over denominator 3 x squared times x squared end fraction times fraction numerator 1 over denominator tan squared invisible function application open parentheses 1 over x close parentheses end fraction close parentheses equals limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator 1 minus 2 x squared over denominator 3 x squared end fraction times fraction numerator 1 over denominator x squared times tan squared invisible function application open parentheses 1 over x close parentheses end fraction close parentheses equals limit as x rightwards arrow straight infinity of invisible function application fraction numerator 1 minus 2 x squared over denominator 3 x squared end fraction times limit as x rightwards arrow straight infinity of invisible function application fraction numerator 1 over denominator x squared times tan squared invisible function application open parentheses 1 over x close parentheses end fraction equals limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator 1 minus 2 x squared over denominator 3 x squared end fraction times fraction numerator 1 over x squared over denominator 1 over x squared end fraction close parentheses times limit as x rightwards arrow straight infinity of invisible function application fraction numerator 1 over denominator x squared times tan squared invisible function application open parentheses 1 over x close parentheses end fraction equals limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator 1 over x squared minus 2 over denominator 3 end fraction close parentheses times limit as x rightwards arrow straight infinity of invisible function application fraction numerator 1 over denominator x squared times tan squared invisible function application open parentheses 1 over x close parentheses end fraction equals open parentheses fraction numerator 0 minus 2 over denominator 3 end fraction close parentheses times limit as x rightwards arrow straight infinity of invisible function application fraction numerator 1 over denominator x squared times tan squared invisible function application open parentheses 1 over x close parentheses end fraction equals negative 2 over 3 times limit as x rightwards arrow straight infinity of invisible function application fraction numerator 1 over denominator x squared times tan squared invisible function application open parentheses 1 over x close parentheses end fraction end style$

Misalkan , maka . Ketika , maka . Sehingga

$begin mathsize 14px style negative 2 over 3 times limit as x rightwards arrow straight infinity of invisible function application fraction numerator 1 over denominator x squared times tan squared invisible function application open parentheses 1 over x close parentheses end fraction equals negative 2 over 3 times limit as y rightwards arrow 0 of invisible function application fraction numerator 1 over denominator open parentheses 1 over y close parentheses squared times tan squared invisible function application y end fraction equals negative 2 over 3 times limit as y rightwards arrow 0 of invisible function application fraction numerator 1 over denominator 1 over y squared times tan squared invisible function application y end fraction equals negative 2 over 3 times limit as y rightwards arrow 0 of invisible function application fraction numerator y squared over denominator tan squared invisible function application y end fraction equals negative 2 over 3 times limit as y rightwards arrow 0 of invisible function application open parentheses fraction numerator y over denominator tan invisible function application y end fraction times fraction numerator y over denominator tan invisible function application y end fraction close parentheses equals negative 2 over 3 times 1 times 1 equals negative 2 over 3 end style$