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Diketahui x→alim​f(x)=−1 dan x→alim​g(x)=6. Tentukan nilai: c. x→alim​(g(x)2−6f(x)2f(x)⋅g(x)​)

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:

c. limit as x rightwards arrow a of open parentheses fraction numerator f left parenthesis x right parenthesis times g left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis squared minus 6 f left parenthesis x right parenthesis squared end fraction close parentheses 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah bold minus bold 1 over bold 5

Ingat!

Jika diketahui limit fungsi aljabar limit 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
  • limit as x rightwards arrow a of open square brackets f left parenthesis x right parenthesis times g left parenthesis x right parenthesis close square brackets equals limit as x rightwards arrow a of f left parenthesis x right parenthesis times limit as x rightwards arrow a of g left parenthesis x right parenthesis equals L times M\
  • limit as x rightwards arrow a of open square brackets fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction close square brackets equals fraction numerator limit as x rightwards arrow a of f left parenthesis x right parenthesis over denominator limit as x rightwards arrow a of g left parenthesis x right parenthesis end fraction equals L over M 

 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow a of open parentheses fraction numerator f left parenthesis x right parenthesis times g left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis squared minus 6 f left parenthesis x right parenthesis squared end fraction close parentheses end cell row blank equals cell fraction numerator limit as x rightwards arrow a of f left parenthesis x right parenthesis times g left parenthesis x right parenthesis over denominator limit as x rightwards arrow a of g left parenthesis x right parenthesis squared minus 6 times f left parenthesis x right parenthesis squared end fraction end cell row blank equals cell fraction numerator limit as x rightwards arrow a of f left parenthesis x right parenthesis times limit as x rightwards arrow a of g left parenthesis x right parenthesis over denominator open parentheses limit as x rightwards arrow a of g left parenthesis x right parenthesis close parentheses squared minus 6 times open parentheses limit as x rightwards arrow a of f left parenthesis x right parenthesis close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses times 6 over denominator 6 squared minus 6 times open parentheses negative 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 6 over denominator 36 minus 6 end fraction end cell row blank equals cell fraction numerator negative 6 over denominator 30 end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 5 end fraction end cell end table 

Dengan demikian,  nilai limit dari limit as x rightwards arrow a of open parentheses fraction numerator f left parenthesis x right parenthesis times g left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis squared minus 6 f left parenthesis x right parenthesis squared end fraction close parentheses, dengan 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 adalah negative 1 fifth.

 

16

5.0 (2 rating)

Idelia Arsanti

Makasih ❤️ Bantu banget

Pertanyaan serupa

Diberikan x→alim​f(x)=3 dan x→alim​g(x)=−1.  Hitunglah nilai setiap limit berikut. a. x→alim​f2(x)+g2(x)​  b. x→alim​f(x)+g(x)2f(x)−3g(x)​  c. x→alim​3g(x)​[f(x)+3]  d. x→alim​[f(x)−3]4

77

4.8

Jawaban terverifikasi

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