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hitunglah

Pertanyaan

hitunglah limit as x rightwards arrow infinity of square root of 4 x squared minus 5 x plus 1 end root minus square root of 4 x squared minus 2 x plus 3 end root

Pembahasan Soal:

Untuk limit tak hingga bentuk akar, dapat diselesaiakan dengan rumus:

limit as straight x rightwards arrow infinity of square root of ax squared plus bx plus straight c end root minus square root of px squared plus qx plus straight r end root equals fraction numerator straight b minus straight q over denominator 2 square root of straight a end fraction comma space untuk space straight a equals straight p

sehingga, untuk fungsi limit

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

diketahui:

a equals 4 comma space b equals negative 5 comma space c equals 1 comma space p equals 4 comma space q equals negative 2 space dan space r equals 3, sehingga:

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

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

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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