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Latihan Tentukan nilai limit dari 3. x → 5 lim ​ 5 − x 4 − x 2 − 9 ​ ​

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Tentukan nilai limit dari

    

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Master Teacher

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diperoleh nilai .

diperoleh nilai limit as x rightwards arrow 5 of space fraction numerator 4 minus square root of x squared minus 9 end root over denominator 5 minus x end fraction equals 5 over 4.

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Perhatikan perhitungan berikut. Jadi diperoleh nilai .

Perhatikan perhitungan berikut.

begin mathsize 14px style limit as x rightwards arrow 5 of space fraction numerator 4 minus square root of x squared minus 9 end root over denominator 5 minus x end fraction equals limit as x rightwards arrow 5 of space fraction numerator 4 minus square root of x squared minus 9 end root over denominator 5 minus x end fraction cross times fraction numerator 4 plus square root of x squared minus 9 end root over denominator 4 plus square root of x squared minus 9 end root end fraction equals limit as x rightwards arrow 5 of space fraction numerator 4 squared minus open parentheses x squared minus 9 close parentheses over denominator open parentheses 5 minus x close parentheses space open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals limit as x rightwards arrow 5 of space fraction numerator 25 minus x squared over denominator open parentheses 5 minus x close parentheses space open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals limit as x rightwards arrow 5 of space fraction numerator open parentheses 5 minus x close parentheses open parentheses 5 plus x close parentheses over denominator open parentheses 5 minus x close parentheses space open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals limit as x rightwards arrow 5 of space fraction numerator open parentheses 5 plus x close parentheses over denominator open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals fraction numerator open parentheses 5 plus 5 close parentheses over denominator open parentheses 4 plus square root of 5 squared minus 9 end root close parentheses end fraction equals 10 over 8 equals 5 over 4 end style 

Jadi diperoleh nilai limit as x rightwards arrow 5 of space fraction numerator 4 minus square root of x squared minus 9 end root over denominator 5 minus x end fraction equals 5 over 4.

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