Pertanyaan

Hitunglah nilai limit-limit berikut ini. d. x → 3 lim x − 3 x 2 − 2 x

Hitunglah nilai limit-limit berikut ini.

d. $x \to 3 lim \frac{x ^{2} - 2 x}{x - 3}$

M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

dapat disimpulkan bahwanilai limit dari tidak ada.

dapat disimpulkan bahwa nilai limit dari $limit as x rightwards arrow 3 of fraction numerator x squared minus 2 x over denominator x minus 3 end fraction$ tidak ada.

Pembahasan

Dihitung limit kanan dan kirinya Diperoleh limit kanan dan limit kirinya tidak sama maka tidak ada. Jadi, dapat disimpulkan bahwanilai limit dari tidak ada.

Dihitung limit kanan dan kirinya

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 to the power of plus of fraction numerator x squared minus 2 x over denominator x minus 3 end fraction end cell equals cell limit as x rightwards arrow 3 to the power of plus of open parentheses x squared minus 2 x close parentheses open parentheses x minus 3 close parentheses to the power of negative 1 end exponent end cell row blank equals cell limit as x rightwards arrow 3 to the power of plus of open parentheses x squared minus 2 x close parentheses times limit as x rightwards arrow 3 to the power of plus of open parentheses x minus 3 close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 9 minus 6 close parentheses times infinity end cell row blank equals infinity end table end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 to the power of minus of fraction numerator x squared minus 2 x over denominator x minus 3 end fraction end cell equals cell limit as x rightwards arrow 3 to the power of minus of open parentheses x squared minus 2 x close parentheses open parentheses x minus 3 close parentheses to the power of negative 1 end exponent end cell row blank equals cell limit as x rightwards arrow 3 to the power of minus of open parentheses x squared minus 2 x close parentheses times limit as x rightwards arrow 3 to the power of minus of open parentheses x minus 3 close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 9 minus 6 close parentheses times open parentheses negative infinity close parentheses end cell row blank equals cell negative infinity end cell end table end style$

Diperoleh limit kanan dan limit kirinya tidak sama maka $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 of end cell end table fraction numerator x squared minus 2 x over denominator x minus 3 end fraction end style$ tidak ada.

Jadi, dapat disimpulkan bahwa nilai limit dari $limit as x rightwards arrow 3 of fraction numerator x squared minus 2 x over denominator x minus 3 end fraction$ tidak ada.