Pertanyaan

Selidiki fungsi tersebut mempunyai lmit atau tidak, berikan alasan! C). x → 0 lim x − x x − x

Selidiki fungsi tersebut mempunyai lmit atau tidak, berikan alasan!

C). $x \to 0 lim \frac{x - x}{x - x}$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

tidak mempunyai limit karena nilai limit kanan limit kiri.

$begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x minus square root of x over denominator x minus square root of x end fraction end style$ tidak mempunyai limit karena nilai limit kanan limit kiri.

Pembahasan

Diketahui , maka: - Untuk - Untuk sehingga: Jadi, tidak mempunyai limit karena nilai limit kanan limit kiri.

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

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

- Untuk

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

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 limit kiri.

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