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Nilai dari

Pertanyaan

Nilai dari limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 5 x minus 3 end root minus 2 x minus 1 close parentheses equals horizontal ellipsis 

Pembahasan Soal:

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 L 

Dimana:

(1) Jika a equals p maka L equals fraction numerator b minus q over denominator 2 square root of a end fraction 

(2) JIka a greater than p maka L equals infinity 

(3) Jika a less than p maka L equals negative infinity 

limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 5 x minus 3 end root minus 2 x minus 1 close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 5 x minus 3 end root minus open parentheses 2 x plus 1 close parentheses close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 5 x minus 3 end root minus square root of open parentheses 2 x plus 1 close parentheses squared end root close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 5 x minus 3 end root minus square root of 4 x squared plus 4 x plus 1 end root close parentheses 

Karena pada soal diatas memenuhi sifat limit tersebut, maka akan digunakan rumus pertama.

L equals fraction numerator b minus q over denominator 2 square root of a end fraction L equals fraction numerator 5 minus 4 over denominator 2 square root of 4 end fraction L equals fraction numerator 1 over denominator 2 cross times 2 end fraction L equals 1 fourth 

Dengan demikian, hasil dari limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 5 x minus 3 end root minus square root of 4 x squared plus 4 x plus 1 end root close parentheses adalah 1 fourth.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 05 Mei 2021

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