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Selidiki fungsi tersebut mempunyai lmit atau tidak, berikan alasan! A).

Selidiki fungsi tersebut mempunyai lmit atau tidak, berikan alasan!

A). begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator open vertical bar x minus 1 close vertical bar over denominator x minus 1 end fraction end style 

Jawaban:

Diketahui begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator open vertical bar x minus 1 close vertical bar over denominator x minus 1 end fraction end style, maka:

- Untuk begin mathsize 14px style x rightwards arrow 1 to the power of plus end style 

begin mathsize 14px style limit as x rightwards arrow 1 to the power of plus of fraction numerator x minus 1 over denominator x minus 1 end fraction equals limit as x rightwards arrow 1 to the power of plus of space 1 equals 1 end style 

- Untuk begin mathsize 14px style x rightwards arrow 1 to the power of minus end style 

begin mathsize 14px style limit as x rightwards arrow 1 to the power of plus of fraction numerator negative open parentheses x minus 1 close parentheses over denominator x minus 1 end fraction equals limit as x rightwards arrow 1 to the power of plus of space open parentheses negative 1 close parentheses equals negative 1 end style 

sehingga:

begin mathsize 14px style limit as x rightwards arrow 1 to the power of plus of fraction numerator open vertical bar x minus 1 close vertical bar over denominator x minus 1 end fraction not equal to limit as x rightwards arrow 1 to the power of minus of fraction numerator open vertical bar x minus 1 close vertical bar over denominator x minus 1 end fraction end style 

Jadi, begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator open vertical bar x minus 1 close vertical bar over denominator x minus 1 end fraction end style tidak mempunyai limit karena nilai limit kanan begin mathsize 14px style not equal to end style limit kiri.

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