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Tentukan nilai limit fungsi

Pertanyaan

Tentukan nilai limit fungsi limit as x rightwards arrow infinity of square root of x squared plus 4 x minus 5 end root minus square root of x squared minus x minus 2 end root

Pembahasan Soal:

Diketahui limit as x rightwards arrow infinity of square root of x squared plus 4 x minus 5 end root minus square root of x squared minus x minus 2 end root.

Ditanya nilai limit fungsi ?

Jawab :
Dengan menggunakan metode mengalikan akar sekawan untuk mencari nilai limit suatu fungsi.

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

Jadi, nilai limit fungsinya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 2 end cell end table.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 09 Juni 2021

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