Pertanyaan

x → 1 lim 4 x 5 − x − 5 + x = ...

$x \to 1 lim \frac{5 - x - 5 + x}{4 x} = ...$

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Habis dalam

Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

$limit as x rightwards arrow 1 of fraction numerator square root of 5 minus square root of x end root minus square root of 5 plus square root of x end root over denominator square root of 4 x end root end fraction equals 0 over 0 comma space k a r e n a space h a s i ln y a space 0 over 0 comma space m a k a space h a r u s space d i r a s i o n a l k a n comma space m e n j a d i colon equals limit as x rightwards arrow 1 of fraction numerator square root of 5 minus square root of x end root minus square root of 5 plus square root of x end root over denominator square root of 4 x end root end fraction equals limit as x rightwards arrow 1 of fraction numerator square root of 5 minus square root of x end root minus square root of 5 plus square root of x end root over denominator square root of 4 x end root end fraction cross times fraction numerator open parentheses open parentheses square root of 5 minus square root of x end root close parentheses plus open parentheses square root of 5 plus square root of x end root close parentheses close parentheses over denominator open parentheses open parentheses square root of 5 minus square root of x end root close parentheses plus open parentheses square root of 5 plus square root of x end root close parentheses close parentheses end fraction equals limit as x rightwards arrow 1 of fraction numerator open parentheses 5 minus square root of x close parentheses minus open parentheses 5 plus square root of x close parentheses over denominator square root of 4 x end root. open parentheses square root of 5 minus square root of x end root close parentheses plus open parentheses square root of 5 plus square root of x end root close parentheses end fraction equals limit as x rightwards arrow 1 of fraction numerator negative 2 square root of x over denominator 2 square root of x. open parentheses square root of 5 minus square root of x end root close parentheses plus open parentheses square root of 5 plus square root of x end root close parentheses end fraction equals limit as x rightwards arrow 1 of fraction numerator negative 1 over denominator open parentheses square root of 5 minus square root of x end root close parentheses plus open parentheses square root of 5 plus square root of x end root close parentheses end fraction equals fraction numerator negative 1 over denominator open parentheses square root of 5 minus square root of 1 end root close parentheses plus open parentheses square root of 5 plus square root of 1 end root close parentheses end fraction equals fraction numerator negative 1 over denominator 2 plus square root of 6 end fraction equals fraction numerator negative 1 over denominator 2 plus square root of 6 end fraction cross times fraction numerator open parentheses 2 minus square root of 6 close parentheses over denominator open parentheses 2 minus square root of 6 close parentheses end fraction equals fraction numerator square root of 6 minus 2 over denominator 4 minus 6 end fraction equals negative 1 half square root of 6 plus 1$