Perhatikan gambar grafik fungsi y=f(x) berikut.   Diketahui a∈{0, 2, 4}. Jika x→alim​f(x) ada, maka nilai a yang memenuhi adalah ...

Pertanyaan

Perhatikan gambar grafik fungsi begin mathsize 14px style bold italic y bold equals bold italic f bold left parenthesis bold italic x bold right parenthesis end style berikut.



 

Diketahui begin mathsize 14px style a element of open curly brackets 0 comma space 2 comma space 4 close curly brackets end style. Jika begin mathsize 14px style limit as x rightwards arrow a of f left parenthesis x right parenthesis end style ada, maka nilai size 14px a yang memenuhi adalah ...

  1. begin mathsize 14px style a equals 0 end style saja

  2. size 14px a size 14px equals size 14px 2 saja

  3. begin mathsize 14px style a equals 0 end style dan size 14px a size 14px equals size 14px 2 

  4. begin mathsize 14px style a equals 0 end style dan size 14px a size 14px equals size 14px 4

  5. begin mathsize 14px style a equals 0 end stylesize 14px a size 14px equals size 14px 2, dan size 14px a size 14px equals size 14px 4 

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ada syarat yang harus dipenuhi agar suatu fungsi memiliki limit di begin mathsize 14px style c end style. Limit size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis di begin mathsize 14px style c end style ada jika dan hanya jika limit kiri dan limit kanan size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis di begin mathsize 14px style c end style ada dan nilainya sama.

Dapat ditulis:

begin mathsize 14px style limit as x rightwards arrow c of f left parenthesis x right parenthesis equals straight L left right arrow limit as x rightwards arrow c to the power of minus of f left parenthesis x right parenthesis equals limit as x rightwards arrow c to the power of plus of f left parenthesis x right parenthesis equals straight L end style 

Sehingga,

Untuk begin mathsize 14px style x end style mendekati 0

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 to the power of minus of f left parenthesis x right parenthesis end cell equals 6 row cell limit as x rightwards arrow 0 to the power of plus of f left parenthesis x right parenthesis end cell equals 6 end table end style 

begin mathsize 14px style Limit space kiri equals limit space kanan end style, akibatnya begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of f left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table end style.

Untuk begin mathsize 14px style x end style mendekati 2

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 to the power of minus of f left parenthesis x right parenthesis end cell equals 2 row cell limit as x rightwards arrow 2 to the power of plus of f left parenthesis x right parenthesis end cell equals 2 end table end style 

begin mathsize 14px style Limit space kiri equals limit space kanan end style, akibatnya begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 2 of f left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table end style.

Untuk begin mathsize 14px style x end style mendekati 4

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 to the power of minus of f left parenthesis x right parenthesis end cell equals 6 row cell limit as x rightwards arrow 4 to the power of plus of f left parenthesis x right parenthesis end cell equals 2 end table end style 

undefined, akibatnya begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 4 of f left parenthesis x right parenthesis end cell end table end style tidak ada.

Jadi, jawaban yang tepat adalah C.

342

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Cahya Ailm

Pembahasan lengkap banget Ini yang aku cari! Mudah dimengerti Bantu banget Makasih ❤️

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