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Nilai dari x→∞lim​(x(4x+5)​−4x2−3​) adalah ...

Pertanyaan

Nilai dari limit as x rightwards arrow infinity of open parentheses square root of x open parentheses 4 x plus 5 close parentheses end root minus square root of 4 x squared minus 3 end root close parentheses adalah ...

  1. 4 over 5 

  2. negative 4 over 5 

  3. 5 over 4 

  4. negative 5 over 4 

  5. 4 

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

ingat konsep limit tak hingga bentuk akar berikut:

limit as x rightwards arrow infinity of open parentheses 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 close parentheses equals open curly brackets table attributes columnalign left end attributes row cell infinity comma space a greater than p end cell row cell fraction numerator b minus q over denominator 2 square root of a end fraction comma space a equals p end cell row cell negative infinity comma space a less than p end cell end table close

maka:

limit as x rightwards arrow infinity of open parentheses square root of x open parentheses 4 x plus 5 close parentheses end root minus square root of 4 x squared minus 3 end root close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 5 x end root minus square root of 4 x squared minus 3 end root space close parentheses equals fraction numerator b minus q over denominator 2 square root of a end fraction equals fraction numerator 5 minus 0 over denominator 2 square root of 4 end fraction equals fraction numerator 5 over denominator 2 times 2 end fraction equals 5 over 4   

Jadi, jawaban yang tepat adalah C.

 

91

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