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Tentukan nilai limit dari: c. x→∞lim​(2x2−5x−3​−2x2−x−3​)

Pertanyaan

Tentukan nilai limit dari:

c. begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of 2 x squared minus 5 x minus 3 end root minus square root of 2 x squared minus x minus 3 end root close parentheses end style

N. Puspita

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Jawaban terverifikasi

Jawaban

 begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of 2 x squared minus 5 x minus 3 end root minus square root of 2 x squared minus x minus 3 end root close parentheses equals negative square root of 2 end style.

Pembahasan

Pada limit tak hingga, misal

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 L L equals fraction numerator b minus q over denominator 2 square root of a end fraction comma space j i k a space a equals p 

maka, nilai limitnya adalah

 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of square root of 2 x squared minus 5 x minus 3 end root minus square root of 2 x squared minus x minus 3 end root end cell row blank equals cell fraction numerator negative 5 minus left parenthesis negative 1 right parenthesis over denominator 2 square root of 2 end fraction end cell row blank equals cell fraction numerator negative 5 plus 1 over denominator 2 square root of 2 end fraction end cell row blank equals cell fraction numerator negative 4 over denominator 2 square root of 2 end fraction end cell row blank equals cell negative fraction numerator 2 over denominator square root of 2 end fraction end cell row blank equals cell negative fraction numerator 2 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell negative 2 over 2 square root of 2 end cell row blank equals cell negative square root of 2 end cell row blank blank blank end table 

Dengan demikian, begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of 2 x squared minus 5 x minus 3 end root minus square root of 2 x squared minus x minus 3 end root close parentheses equals negative square root of 2 end style.

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