Roboguru

Diketahui , nilai  adalah ...

Pertanyaan

Diketahui f open parentheses x close parentheses equals open curly brackets table attributes columnalign left end attributes row cell 2 x plus 1 comma space untuk space x less than 3 end cell row cell 3 x comma space untuk space x greater or equal than 3 end cell end table close, nilai limit as blank of space f left parenthesis x right parenthesis adalah ...space

Pembahasan Soal:

Suatu limit dikatakan ada (mempunyai nilai) jika limit kanan sama dengan limit kiri.

limit as x rightwards arrow a of f open parentheses x close parentheses equals L left right arrow limit as x rightwards arrow a to the power of minus of f open parentheses x close parentheses equals limit as x rightwards arrow a to the power of plus of f open parentheses x close parentheses  

Diketahui f open parentheses x close parentheses equals open curly brackets table attributes columnalign left end attributes row cell 2 x plus 1 comma space untuk space x less than 3 end cell row cell 3 x comma space untuk space x greater or equal than 3 end cell end table close.

Tentukan limit kiri

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow a to the power of minus of f open parentheses x close parentheses end cell row blank equals cell limit as x rightwards arrow 3 to the power of minus of 2 x plus 1 end cell row blank equals cell 2 open parentheses negative 3 close parentheses plus 1 end cell row blank equals cell negative 5 end cell end table 

Tentukan limit kanan 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow a to the power of plus of f open parentheses x close parentheses end cell row blank equals cell limit as x rightwards arrow 3 to the power of plus of 3 x end cell row blank equals cell 3 times 3 end cell row blank equals 9 end table 

Karena table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 to the power of minus of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x plus 1 end cell end table not equal to table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 to the power of plus of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table, maka 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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank left parenthesis end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank right parenthesis end table tidak ada.

Jadi, 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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank left parenthesis end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank right parenthesis end table tidak ada.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni Universitas Indraprasta PGRI

Terakhir diupdate 06 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui fungsi  sebagai berikut   Nilai

Pembahasan Soal:

Fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style memiliki nilai limit pada titik begin mathsize 14px style c end style jika dan hanya jika nilai limit fungsi tersebut jika didekati dari arah kiri titik undefined dan arah kanan titik size 14px c memiliki nilai yang sama.

begin mathsize 14px style limit as x rightwards arrow c to the power of minus of f open parentheses x close parentheses equals limit as x rightwards arrow c to the power of plus of f open parentheses x close parentheses equals f open parentheses c close parentheses end style

maka begin mathsize 14px style limit as x rightwards arrow c of f open parentheses x close parentheses equals f open parentheses c close parentheses end style

Dengan demikian:

Untuk limit begin mathsize 14px style x equals negative 2 end style dari kiri begin mathsize 14px style open parentheses x less than negative 2 close parentheses end style :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 to the power of minus of f open parentheses x close parentheses end cell equals cell limit as x rightwards arrow negative 2 to the power of minus of open parentheses x squared minus 1 close parentheses end cell row blank equals cell open parentheses 2 close parentheses squared minus 1 end cell row blank equals 3 end table end style 

Untuk limit undefined dari kanan begin mathsize 14px style open parentheses x greater than 2 close parentheses end style :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 to the power of plus of f open parentheses x close parentheses end cell equals cell limit as x rightwards arrow negative 2 to the power of plus of open parentheses negative 2 x minus 1 close parentheses end cell row blank equals cell open parentheses negative 2 open parentheses 2 close parentheses minus 1 close parentheses end cell row blank equals cell negative 5 end cell end table end style 

Berdasarkan perhitungan di atas diperoleh limit kiribegin mathsize 14px style not equal to end style limit kanan

Sehingga, begin mathsize 14px style limit as x rightwards arrow negative 2 of f open parentheses x close parentheses end style tidak ada.

Oleh karena itu, jawaban yang benar adalah E.

0

Roboguru

Tunjukkan pada gambar berikut, fungsi  mempunyai nilai limit atau tidak pada saat  mendekati ! Berikan alasan!

Pembahasan Soal:

Fungsi begin mathsize 14px style y equals f left parenthesis x right parenthesis end style tidak mempunyai limit pada saat undefined mendekati undefined karena nilai fungsi pada saat undefined mendekati undefined dari kiri dan saat undefined mendekati undefined dari kanan nilainya berbeda.

0

Roboguru

Tentukan nilai  yang memenuhi agar fungsi  berikut mempunyai limit. b.

Pembahasan Soal:

agar begin mathsize 14px style f open parentheses x close parentheses end style mempunyai nilai limit maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a to the power of minus of f open parentheses x close parentheses end cell equals cell limit as x rightwards arrow a to the power of plus of f open parentheses x close parentheses space end cell row cell 1 half open parentheses a close parentheses plus 6 end cell equals cell 2 open parentheses a close parentheses plus 21 over 2 end cell row cell a over 2 plus 6 end cell equals cell 2 a plus 21 over 2 end cell row cell a over 2 minus 2 a end cell equals cell 21 over 2 minus 6 end cell row cell fraction numerator negative 3 a over denominator 2 end fraction end cell equals cell 9 over 2 end cell row cell negative 3 a end cell equals 9 row a equals cell negative 3 end cell end table end style 

Jadi nilai undefined yang memenuhi adalah -3

0

Roboguru

Tentukan nilai  yang memenuhi agar fungsi  berikut mempunyai limit. c.

Pembahasan Soal:

agar undefined mempunyai nilai limit maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a to the power of minus of f open parentheses x close parentheses end cell equals cell limit as x rightwards arrow a to the power of plus of f open parentheses x close parentheses end cell row cell open parentheses a close parentheses squared minus 4 end cell equals cell open parentheses a close parentheses plus 2 end cell row cell a squared minus 4 end cell equals cell a plus 2 end cell row cell a squared minus a minus 6 end cell equals 0 row cell open parentheses a minus 3 close parentheses open parentheses a plus 2 close parentheses end cell equals 0 row cell a minus 3 end cell equals cell 0 space space space space a t a u space a plus 2 equals 0 end cell row a equals cell 3 space space space space space space space space space space space space space space space space space space space a equals negative 2 end cell row blank blank blank end table end style 

Jadi nilai undefined yang memenuhi adalah undefined dan 3 

0

Roboguru

Hitunglah nilai limit-limit berikut ini. d.

Pembahasan Soal:

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. 

0

Roboguru

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