Roboguru

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

Selidiki fungsi tersebut mempunyai lmit atau tidak, berikan alasan!

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

Jawaban:

Diketahui begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x minus square root of x over denominator x minus square root of 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 x minus square root of x over denominator x minus square root of x end fraction equals limit as x rightwards arrow 0 to the power of plus of fraction numerator x minus square root of x over denominator x minus square root of x end fraction. fraction numerator x plus square root of x over denominator x plus square root of x end fraction equals limit as x rightwards arrow 0 to the power of plus of fraction numerator x squared minus x over denominator x squared minus x end fraction equals limit as x rightwards arrow 0 to the power of plus of 1 equals 1 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 x minus square root of x over denominator x minus square root of x end fraction equals limit as x rightwards arrow 0 to the power of minus of fraction numerator negative open parentheses x minus square root of x close parentheses over denominator x minus square root of x end fraction. fraction numerator x plus square root of x over denominator x plus square root of x end fraction equals limit as x rightwards arrow 0 to the power of minus of fraction numerator negative open parentheses x squared minus x close parentheses over denominator x squared minus x end fraction equals limit as x rightwards arrow 0 to the power of plus of open parentheses negative 1 close parentheses equals negative 1 end style 

sehingga:

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

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