Tentukan nilai limit berikut. a. x→5lim(−2x+7)7

Diketahui dan nilai limit berikut. Nilai limit yang benar adalah ...

Pembahasan Soal:

Ingatlah sifat-sifat limit fungsi untuk menjawab soal di atas.

Akan dicoba satu-satu pernyataan pada soal apakah benar atau tidak. Diketahui $limit as straight x rightwards arrow 2 of invisible function application straight f left parenthesis straight x right parenthesis equals 3$ maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight i right parenthesis space space limit as straight x rightwards arrow 2 of invisible function application open square brackets straight f left parenthesis straight x right parenthesis minus straight f squared left parenthesis straight x right parenthesis close square brackets end cell equals cell limit as straight x rightwards arrow 2 of invisible function application f left parenthesis x right parenthesis minus open square brackets limit as straight x rightwards arrow 2 of invisible function application minus straight f left parenthesis straight x right parenthesis close square brackets squared end cell row blank equals cell 3 minus open parentheses 3 close parentheses squared end cell row blank equals cell 3 minus 9 end cell row blank equals cell negative 6. end cell end table$

Pernyataan (i) salah.

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis ii right parenthesis space space limit as straight x rightwards arrow 2 of invisible function application open square brackets open parentheses straight f left parenthesis straight x right parenthesis plus 2 close parentheses squared minus 4 space straight f left parenthesis straight x right parenthesis close square brackets end cell equals cell open square brackets space limit as straight x rightwards arrow 2 of invisible function application straight f left parenthesis straight x right parenthesis plus 2 close square brackets squared minus 4 limit as straight x rightwards arrow 2 of invisible function application straight f left parenthesis straight x right parenthesis end cell row blank equals cell open square brackets space limit as straight x rightwards arrow 2 of invisible function application straight f left parenthesis straight x right parenthesis plus space limit as straight x rightwards arrow 2 of invisible function application 2 close square brackets squared minus 4 limit as straight x rightwards arrow 2 of invisible function application straight f left parenthesis straight x right parenthesis end cell row blank equals cell open square brackets 3 plus 2 close square brackets squared minus 4 open parentheses 3 close parentheses end cell row blank equals cell 25 minus 12 end cell row blank equals cell 13. end cell end table$

Pernyataan (ii) benar.

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis iii right parenthesis space space limit as straight x rightwards arrow 2 of invisible function application open square brackets straight f left parenthesis straight x right parenthesis minus 2 straight x plus 4 close square brackets squared end cell equals cell space limit as straight x rightwards arrow 2 of invisible function application open square brackets straight f left parenthesis straight x right parenthesis minus 2 straight x plus 4 close square brackets squared end cell row blank equals cell open square brackets limit as straight x rightwards arrow 2 of invisible function application straight f left parenthesis straight x right parenthesis minus 2 straight x plus 4 close square brackets squared end cell row blank equals cell open square brackets limit as straight x rightwards arrow 2 of invisible function application straight f left parenthesis straight x right parenthesis minus 2 limit as straight x rightwards arrow 2 of invisible function application straight x plus limit as straight x rightwards arrow 2 of invisible function application 4 close square brackets squared end cell row blank equals cell open square brackets 3 minus 2 open parentheses 2 close parentheses plus 4 close square brackets squared end cell row blank equals cell open square brackets 3 minus 4 plus 4 close square brackets squared end cell row blank equals cell 9. end cell end table$

Pertanyaan (iii) salah.

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis iv right parenthesis space space limit as straight x rightwards arrow 2 of invisible function application cube root of 4 straight f squared left parenthesis straight x right parenthesis minus 9 end root end cell equals cell open square brackets limit as straight x rightwards arrow 2 of invisible function application 4 straight f squared left parenthesis straight x right parenthesis minus 9 close square brackets to the power of 1 third end exponent end cell row blank equals cell open square brackets 4 limit as straight x rightwards arrow 2 of invisible function application straight f squared left parenthesis straight x right parenthesis minus limit as straight x rightwards arrow 2 of invisible function application 9 close square brackets to the power of 1 third end exponent end cell row blank equals cell open square brackets 4 open parentheses limit as straight x rightwards arrow 2 of invisible function application straight f left parenthesis straight x right parenthesis close parentheses squared minus limit as straight x rightwards arrow 2 of invisible function application 9 close square brackets to the power of 1 third end exponent end cell row blank equals cell open square brackets 4 open parentheses 3 close parentheses squared minus 9 close square brackets to the power of 1 third end exponent end cell row blank equals cell cube root of 36 minus 9 end root end cell row blank equals cell cube root of 27 end cell row blank equals cell 3. end cell end table$

Pertanyaan (iv) benar.

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight v right parenthesis space space space limit as straight x rightwards arrow 2 of invisible function application fraction numerator straight f left parenthesis straight x right parenthesis plus 9 over denominator 1 minus straight f left parenthesis straight x right parenthesis end fraction end cell equals cell fraction numerator limit as straight x rightwards arrow 2 of invisible function application straight f left parenthesis straight x right parenthesis plus 9 over denominator limit as straight x rightwards arrow 2 of invisible function application 1 minus straight f left parenthesis straight x right parenthesis end fraction end cell row blank equals cell fraction numerator limit as straight x rightwards arrow 2 of invisible function application straight f left parenthesis straight x right parenthesis plus limit as straight x rightwards arrow 2 of invisible function application 9 over denominator limit as straight x rightwards arrow 2 of invisible function application 1 minus limit as straight x rightwards arrow 2 of invisible function application straight f left parenthesis straight x right parenthesis end fraction end cell row blank equals cell fraction numerator 3 plus 9 over denominator 1 minus 3 end fraction end cell row blank equals cell fraction numerator 12 over denominator negative 2 end fraction end cell row blank equals cell negative 6. end cell end table$

Pernyataan (v) benar.

Berdasarkan uraian di atas, maka pernyataan yang benar adalah (ii), (iv), dan (v).

Oleh karena itu, jawaban yang benar adalah D.

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