Diketahui x→alim​ f(x)=2 dan x→alim​ [2f(x)2+3g(x)2]=11. Nilai dari x→alim​ g(x) adalah ....

Pertanyaan

Diketahui limit as x rightwards arrow a of space f open parentheses x close parentheses equals 2 dan limit as x rightwards arrow a of space open square brackets 2 f open parentheses x close parentheses squared plus 3 g open parentheses x close parentheses squared close square brackets equals 11. Nilai dari limit as x rightwards arrow a of space g open parentheses x close parentheses adalah ....

  1. 1

  2. 2

  3. 3

  4. 4

  5. 5

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Jawaban yang benar adalah A.

Ingat kembali mengenai sifat-sifat limit di bawah ini.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a of space open square brackets k times f open parentheses x close parentheses close square brackets end cell equals cell k times limit as x rightwards arrow a of f open parentheses x close parentheses end cell row blank blank blank end table

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a of space open square brackets f open parentheses x close parentheses plus g open parentheses x close parentheses close square brackets end cell equals cell limit as x rightwards arrow a of f open parentheses x close parentheses plus limit as x rightwards arrow a of g open parentheses x close parentheses end cell row blank blank blank end table

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a of space open square brackets f open parentheses x close parentheses close square brackets to the power of n end cell equals cell open parentheses limit as x rightwards arrow a of f open parentheses x close parentheses close parentheses to the power of n end cell row blank blank blank end table

 

Dengan menggunakan sifat limit di atas, ubah bentuk limit as x rightwards arrow a of space open square brackets 2 f open parentheses x close parentheses squared plus 3 g open parentheses x close parentheses squared close square brackets equals 11, kemudian subtitusikan limit as x rightwards arrow a of space f open parentheses x close parentheses equals 2 untuk mendapatkan nilai limit as x rightwards arrow a of space g open parentheses x close parentheses.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a of space open square brackets 2 f open parentheses x close parentheses squared plus 3 g open parentheses x close parentheses squared close square brackets end cell equals 11 row cell open parentheses limit as x rightwards arrow a of space 2 f open parentheses x close parentheses squared close parentheses plus open parentheses limit as x rightwards arrow a of space 3 g open parentheses x close parentheses squared close parentheses end cell equals 11 row cell 2 times open parentheses limit as x rightwards arrow a of space f open parentheses x close parentheses close parentheses squared plus 3 times open parentheses limit as x rightwards arrow a of g open parentheses x close parentheses close parentheses squared end cell equals 11 row cell 2 times open parentheses 2 close parentheses squared plus 3 times open parentheses limit as x rightwards arrow a of g open parentheses x close parentheses close parentheses squared end cell equals 11 row cell 8 plus 3 times open parentheses limit as x rightwards arrow a of g open parentheses x close parentheses close parentheses squared end cell equals 11 row cell 3 times open parentheses limit as x rightwards arrow a of g open parentheses x close parentheses close parentheses squared end cell equals cell 11 minus 8 end cell row cell open parentheses limit as x rightwards arrow a of g open parentheses x close parentheses close parentheses squared end cell equals cell 3 over 3 end cell row cell limit as x rightwards arrow a of g open parentheses x close parentheses end cell equals cell square root of 1 end cell row cell limit as x rightwards arrow a of g open parentheses x close parentheses end cell equals 1 end table

Jadi, nilai dari limit as x rightwards arrow a of space g open parentheses x close parentheses adalah 1.

Oleh karena itu, jawaban yang benar adalah A.

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