Roboguru

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

Selidiki fungsi tersebut mempunyai lmit atau tidak, berikan alasan!

B). begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of x over denominator x end fraction end style 

Jawaban:

Diketahui begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of x over denominator x end fraction end style , maka:

- Untuk begin mathsize 14px style x rightwards arrow 0 to the power of plus end style 

begin mathsize 14px style limit as x rightwards arrow 0 to the power of plus of fraction numerator square root of x over denominator x end fraction equals limit as x rightwards arrow 0 to the power of plus of fraction numerator square root of x over denominator x end fraction times fraction numerator square root of x over denominator square root of x end fraction equals limit as x rightwards arrow 0 to the power of plus of fraction numerator x over denominator x square root of x end fraction equals limit as x rightwards arrow 0 to the power of plus of fraction numerator 1 over denominator square root of x end fraction equals infinity end style  

- Untuk begin mathsize 14px style x rightwards arrow 0 to the power of minus end style 

begin mathsize 14px style limit as x rightwards arrow 0 to the power of minus of fraction numerator negative square root of x over denominator x end fraction equals limit as x rightwards arrow 0 to the power of minus of fraction numerator negative square root of x over denominator x end fraction times fraction numerator square root of x over denominator square root of x end fraction equals limit as x rightwards arrow 0 to the power of minus of fraction numerator negative x over denominator x square root of x end fraction equals limit as x rightwards arrow 0 to the power of minus of fraction numerator negative 1 over denominator square root of x end fraction equals negative infinity end style 

sehingga:

begin mathsize 14px style limit as x rightwards arrow 0 to the power of plus of fraction numerator square root of x over denominator x end fraction not equal to limit as x rightwards arrow 0 to the power of minus of fraction numerator square root of x over denominator x end fraction end style 

Jadi, begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of x over denominator x 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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