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Diketahui x→alim​f(x)=−1 dan x→alim​g(x)=6. Tentukan nilai: b. x→alim​[4f(x)2+g(x)2]

Pertanyaan

Diketahui limit as x rightwards arrow a of f left parenthesis x right parenthesis equals negative 1 dan limit as x rightwards arrow a of g left parenthesis x right parenthesis equals 6.

Tentukan nilai:

b. limit as x rightwards arrow a of open square brackets 4 f left parenthesis x right parenthesis squared plus g left parenthesis x right parenthesis squared close square brackets 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow a of open square brackets 4 f left parenthesis x right parenthesis squared plus g left parenthesis x right parenthesis squared close square brackets end cell end table adalah 40.

Pembahasan

Jawaban yang benar untuk pertanyaan 10, b. adalah bold 40.

Ingat!

Jika diketahui limit fungsi aljabarlimit as x rightwards arrow a of f left parenthesis x right parenthesis equals L dan limit as x rightwards arrow a of g left parenthesis x right parenthesis equals M, serta bilangan real c, maka:

  • limit as x rightwards arrow a of open square brackets f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis close square brackets equals limit as x rightwards arrow a of f left parenthesis x right parenthesis plus limit as x rightwards arrow a of g left parenthesis x right parenthesis equals L plus M
  • limit as x rightwards arrow a of open square brackets c f left parenthesis x right parenthesis close square brackets equals c times limit as x rightwards arrow a of f left parenthesis x right parenthesis equals c times L 
  • limit as x rightwards arrow a of open parentheses f left parenthesis x right parenthesis close parentheses to the power of n equals open parentheses limit as x rightwards arrow a of f left parenthesis x right parenthesis close parentheses to the power of n equals L to the power of n

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow a of open square brackets 4 f left parenthesis x right parenthesis squared plus g left parenthesis x right parenthesis squared close square brackets end cell row blank equals cell 4 open parentheses limit as x rightwards arrow a of f left parenthesis x right parenthesis close parentheses squared space plus open parentheses limit as x rightwards arrow a of g left parenthesis x right parenthesis close parentheses squared end cell row blank equals cell 4 times left parenthesis negative 1 right parenthesis squared plus 6 to the power of 2 end exponent end cell row blank equals cell 4 plus 36 end cell row blank equals 40 end table

Dengan demikian, nilai dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow a of open square brackets 4 f left parenthesis x right parenthesis squared plus g left parenthesis x right parenthesis squared close square brackets end cell end table adalah 40.

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Jawaban terverifikasi

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