x→∞lim​x2−2x+1​−x2+3x+2​=…

Pertanyaan

limit as x rightwards arrow infinity of square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x plus 2 end root equals horizontal ellipsis 

  1. 6 1 half 

  2. negative 2 

  3. negative 2 1 half 

  4. 4 1 half 

  5. 3 1 half 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Pembahasan

Perhatikan cara hitung limit tak hingga berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank space row blank blank blank end table             limit as x rightwards arrow infinity of square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root equals open curly brackets table attributes columnalign left end attributes row cell infinity comma space jika space a greater than c end cell row cell fraction numerator b minus q over denominator 2 square root of a end fraction comma space jika space a equals c end cell row cell negative infinity comma space jika space a less than c end cell end table close          

Pada soal a equals c equals 1, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x plus 2 end root end cell equals cell fraction numerator b minus q over denominator 2 square root of a end fraction end cell row blank equals cell fraction numerator open parentheses negative 2 close parentheses minus 3 over denominator 2 square root of 1 end fraction end cell row blank equals cell negative 5 over 2 end cell row blank equals cell negative 2 1 half end cell end table  

Jadi, jawaban yang tepat adalah C.

164

4.5 (8 rating)

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