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l im ┬ ( x → 0 ) 〖 ( √ ( 1 + √ x ) − √ ( 1 − √ x ) ) /√2 x 〗 = ...

...

  1. 1 divided by 2

  2. 1 divided by 3

  3. 1 divided by 2 space √ 2

  4. 1 divided by 2 space √ 3

  5. 1 divided by 3 space √ 2

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N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

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l i m ┬ left parenthesis x rightwards arrow 0 right parenthesis invisible function application 〖 left parenthesis space √ left parenthesis 1 plus √ x right parenthesis space minus √ left parenthesis 1 minus √ x right parenthesis space right parenthesis divided by √ 2 x 〗 equals l i m ┬ left parenthesis x rightwards arrow 0 right parenthesis invisible function application 〖 left parenthesis space √ left parenthesis 1 plus √ x right parenthesis space minus √ left parenthesis 1 minus √ x right parenthesis space right parenthesis divided by √ 2 x 〗 cross times left parenthesis √ left parenthesis 1 plus √ x right parenthesis space plus √ left parenthesis 1 minus √ x right parenthesis space right parenthesis divided by left parenthesis √ left parenthesis 1 plus √ x right parenthesis space plus √ left parenthesis 1 minus √ x right parenthesis space right parenthesis

equals l i m ┬ left parenthesis x rightwards arrow 0 right parenthesis invisible function application 〖 left parenthesis space 1 right parenthesis divided by √ 2 x 〗 cross times left parenthesis left parenthesis 1 plus √ x right parenthesis minus left parenthesis 1 minus √ x right parenthesis right parenthesis divided by left parenthesis √ left parenthesis 1 plus √ x right parenthesis space plus √ left parenthesis 1 minus √ x right parenthesis space right parenthesis

equals l i m ┬ left parenthesis x rightwards arrow 0 right parenthesis invisible function application 〖 left parenthesis space 1 right parenthesis divided by left parenthesis √ 2 space space √ x right parenthesis 〗 cross times left parenthesis 2 √ x right parenthesis divided by left parenthesis √ left parenthesis 1 plus √ x right parenthesis space plus √ left parenthesis 1 minus √ x right parenthesis space right parenthesis

equals l i m ┬ left parenthesis x rightwards arrow 0 right parenthesis invisible function application 〖 left parenthesis space 1 right parenthesis divided by left parenthesis √ 2 space space right parenthesis 〗 cross times 2 divided by left parenthesis √ left parenthesis 1 plus √ x right parenthesis space plus √ left parenthesis 1 minus √ x right parenthesis space right parenthesis

equals left parenthesis space 1 right parenthesis divided by left parenthesis √ 2 space space right parenthesis cross times 2 divided by left parenthesis √ left parenthesis 1 plus √ 0 right parenthesis space plus √ left parenthesis 1 minus √ 0 right parenthesis space right parenthesis

equals left parenthesis space 1 right parenthesis divided by left parenthesis √ 2 space space right parenthesis cross times 2 divided by 2

equals 1 divided by √ 2 cross times √ 2 divided by √ 2

equals 1 divided by 2 space √ 2

 

 

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